## STACK Documentation

Documentation home | Category index | Site map# Int: Answer test results

This page exposes the results of running answer tests on STACK test cases. This page is automatically generated from the STACK unit tests and is designed to show question authors what answer tests actually do. This includes cases where answer tests currentl fail, which gives a negative expected mark. Comments and further test cases are very welcome.

## Int

Test | ? | Student response | Teacher answer | Opt | Mark | Answer note | |
---|---|---|---|---|---|---|---|

Int | 1/0 |
1 |
-1 | STACKERROR_OPTION. | |||

TEST_FAILED | |||||||

The answer test failed to execute correctly: please alert your teacher. Missing option when executing the test. | |||||||

Int | 1/0 |
1 |
x |
-1 | ATInt_STACKERROR_SAns. | ||

Int | 1 |
1/0 |
x |
-1 | ATInt_STACKERROR_TAns. | ||

Int | 0 |
0 |
1/0 |
-1 | ATInt_STACKERROR_Opt. | ||

Int | 0 |
0 |
[x,1/0] |
-1 | ATInt_STACKERROR_Opt. | ||

Int | 0 |
0 |
[x,NOCONST,1/0] |
-1 | ATInt_STACKERROR_Opt. | ||

Basic tests | |||||||

Int | x^3/3 |
x^3/3 |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | x^3/3+1 |
x^3/3 |
x |
0 | ATInt_const_int. | ||

You need to add a constant of integration. This should be an arbitrary constant, not a number. | |||||||

Int | x^3/3+c |
x^3/3 |
x |
1 | ATInt_true. | ||

Int | x^3/3-c |
x^3/3 |
x |
1 | ATInt_true. | ||

Int | x^3/3+c+1 |
x^3/3 |
x |
1 | ATInt_true. | ||

Int | x^3/3+3*c |
x^3/3 |
x |
1 | ATInt_true. | ||

Int | (x^3+c)/3 |
x^3/3 |
x |
1 | ATInt_true. | ||

Int | x^(k+1)/(k+1) |
x^(k+1)/(k+1) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | x^(k+1)/(k+1)+c |
x^(k+1)/(k+1) |
x |
1 | ATInt_true. | ||

Int | ! | (x^(k+1)-1)/(k+1) |
x^(k+1)/(k+1) |
x |
-2 | ATInt_true. | |

Int | ! | (x^(k+1)-1)/(k+1)+c |
x^(k+1)/(k+1)+c |
x |
-3 | ATInt_weirdconst. | |

The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this. | |||||||

Int | x^3/3+c+k |
x^3/3 |
x |
0 | ATInt_weirdconst. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this. | |||||||

Int | x^3/3+c^2 |
x^3/3 |
x |
0 | ATInt_weirdconst. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, you have a strange constant of integration. Please ask your teacher about this. | |||||||

Int | x^3/3+c^3 |
x^3/3 |
x |
0 | ATInt_weirdconst. | ||

Int | x^3/3*c |
x^3/3 |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x^2\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[c\\cdot x^2\\] so you must have done something wrong! | |||||||

Int | X^3/3+c |
x^3/3 |
x |
0 | ATInt_generic. ATInt_var_SB_notSA. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x^2\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[0\\] so you must have done something wrong! | |||||||

Int | sin(2*x) |
x^3/3 |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x^2\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[2\\cdot \\cos \\left( 2\\cdot x \\right)\\] so you must have done something wrong! | |||||||

Int | x^2/2-2*x+2+c |
(x-2)^2/2 |
x |
1 | ATInt_true. | ||

Int | (t-1)^5/5+c |
(t-1)^5/5 |
t |
1 | ATInt_true. | ||

Int | (v-1)^5/5+c |
(v-1)^5/5 |
v |
1 | ATInt_true. | ||

Int | cos(2*x)/2+1+c |
cos(2*x)/2 |
x |
1 | ATInt_true. | ||

Int | (x-a)^6001/6001+c |
(x-a)^6001/6001 |
x |
1 | ATInt_true. | ||

Int | (x-a)^6001/6001 |
(x-a)^6001/6001 |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | 6000*(x-a)^5999 |
(x-a)^6001/6001 |
x |
0 | ATInt_diff. | ||

It looks like you have differentiated instead! | |||||||

Int | 4*%e^(4*x)/(%e^(4*x)+1) |
log(%e^(4*x)+1)+c |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\frac{4\\cdot e^{4\\cdot x}}{e^{4\\cdot x}+1}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[\\frac{16\\cdot e^{4\\cdot x}}{e^{4\\cdot x}+1}-\\frac{16\\cdot e^{8 \\cdot x}}{{\\left(e^{4\\cdot x}+1\\right)}^2}\\] so you must have done something wrong! | |||||||

The teacher adds a constant | |||||||

Int | x^3/3+c |
x^3/3+c |
x |
1 | ATInt_true. | ||

Int | x^2/2-2*x+2+c |
(x-2)^2/2+k |
x |
1 | ATInt_true. | ||

The teacher condones lack of constant, or numerical constant | |||||||

Int | x^3/3 |
x^3/3 |
[x,NOCONST] |
1 | ATInt_const_condone. | ||

Int | x^3/3+c |
x^3/3 |
[x,NOCONST] |
1 | ATInt_true. | ||

Int | x^2/2-2*x+2 |
(x-2)^2/2+k |
[x,NOCONST] |
1 | ATInt_const_condone. | ||

Int | x^3/3+1 |
x^3/3 |
[x,NOCONST] |
1 | ATInt_const_int_condone. | ||

Int | x^3/3+c^2 |
x^3/3 |
[x,NOCONST] |
0 | ATInt_weirdconst. | ||

Int | n*x^n |
n*x^(n-1) |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\left(n-1\\right)\\cdot n\\cdot x^{n-2}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[n^2\\cdot x^{n-1}\\] so you must have done something wrong! | |||||||

Int | n*x^n |
(assume(n>0), n*x^(n-1)) |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\left(n-1\\right)\\cdot n\\cdot x^{n-2}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[n^2\\cdot x^{n-1}\\] so you must have done something wrong! | |||||||

Special case | |||||||

Int | exp(x)+c |
exp(x) |
x |
1 | ATInt_true. | ||

Int | exp(x) |
exp(x) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | exp(x) |
exp(x) |
[x,NOCONST] |
1 | ATInt_const_condone. | ||

Student differentiates by mistake | |||||||

Int | 2*x |
x^3/3 |
x |
0 | ATInt_diff. | ||

It looks like you have differentiated instead! | |||||||

Int | 2*x+c |
x^3/3 |
x |
0 | ATInt_diff. | ||

It looks like you have differentiated instead! | |||||||

Sloppy logs (teacher ignores abs(x) ) | |||||||

Int | ln(x) |
ln(x) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | ln(x) |
ln(x) |
[x,NOCONST] |
1 | ATInt_const_condone. | ||

Int | ln(x)+c |
ln(x)+c |
x |
1 | ATInt_true_equiv. | ||

Int | ln(k*x) |
ln(x)+c |
x |
1 | ATInt_true_equiv. | ||

Fussy logs (teacher uses abs(x) ) | |||||||

Int | ln(x) |
ln(abs(x))+c |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \\(\\int\\frac{1}{x} dx = \\log(|x|)+c\\), rather than \\(\\int\\frac{1}{x} dx = \\log(x)+c\\). Please ask your teacher about this. | |||||||

Int | ln(x)+c |
ln(abs(x))+c |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \\(\\int\\frac{1}{x} dx = \\log(|x|)+c\\), rather than \\(\\int\\frac{1}{x} dx = \\log(x)+c\\). Please ask your teacher about this. | |||||||

Int | ln(x) |
ln(abs(x))+c |
[x, NOCONST] |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. Your teacher may expect you to use the result \\(\\int\\frac{1}{x} dx = \\log(|x|)+c\\), rather than \\(\\int\\frac{1}{x} dx = \\log(x)+c\\). Please ask your teacher about this. | |||||||

Int | ln(abs(x)) |
ln(abs(x))+c |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | ln(abs(x))+c |
ln(abs(x))+c |
x |
1 | ATInt_true_equiv. | ||

Int | ln(k*x) |
ln(abs(x))+c |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | ln(k*abs(x)) |
ln(abs(x))+c |
x |
1 | ATInt_true_equiv. | ||

Int | ln(abs(k*x)) |
ln(abs(x))+c |
x |
1 | ATInt_true_equiv. | ||

Teacher uses ln(k*abs(x)) | |||||||

Int | ln(x) |
ln(k*abs(x)) |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | ln(x)+c |
ln(k*abs(x)) |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | ln(abs(x)) |
ln(k*abs(x)) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | ln(abs(x))+c |
ln(k*abs(x)) |
x |
1 | ATInt_true_equiv. | ||

Int | ln(k*x) |
ln(k*abs(x)) |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | ln(k*abs(x)) |
ln(k*abs(x)) |
x |
1 | ATInt_true_equiv. | ||

Other logs | |||||||

Int | ln(x)+ln(a) |
ln(k*abs(x+a)) |
x |
0 | ATInt_generic. ATInt_logabs. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\frac{1}{x+a}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[\\frac{1}{x}\\] so you must have done something wrong! Your teacher may expect you to use the result \\(\\int\\frac{1}{x} dx = \\log(|x|)+c\\), rather than \\(\\int\\frac{1}{x} dx = \\log(x)+c\\). Please ask your teacher about this. | |||||||

Int | log(x)^2-2*log(c)*log(x)+k |
ln(c/x)^2 |
x |
0 | ATInt_EqFormalDiff. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. | |||||||

Int | log(x)^2-2*log(c)*log(x)+k |
ln(abs(c/x))^2 |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[-\\frac{2\\cdot \\ln \\left( \\frac{\\left| c\\right| }{\\left| x\\right| } \\right)}{x}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[\\frac{2\\cdot \\ln \\left( x \\right)}{x}-\\frac{2\\cdot \\ln \\left( c \\right)}{x}\\] so you must have done something wrong! | |||||||

Int | c-(log(2)-log(x))^2/2 |
-1/2*log(2/x)^2 |
x |
1 | ATInt_true_equiv. | ||

Int | ln(abs(x+3))/2+c |
ln(abs(2*x+6))/2+c |
x |
0 | ATInt_EqFormalDiff. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. | |||||||

Int | ln(abs(x+3))/2+c |
ln(abs(2*x+6))/2+c |
[x, FORMAL] |
1 | ATInt_EqFormalDiff. | ||

The formal derivative of your answer does equal the expression that you were asked to integrate. However, your answer differs from the correct answer in a significant way, that is to say not just, e.g., a constant of integration. Please ask your teacher about this. | |||||||

Int | ln(abs(x+3))/2 |
ln(abs(2*x+6))/2+c |
[x, FORMAL] |
1 | ATInt_EqFormalDiff. | ||

Int | ln(abs(x+3))/2 |
ln(abs(2*x+6))/2+c |
[x, FORMAL, NOC ONST] |
1 | ATInt_EqFormalDiff. | ||

Int | ln(abs(x+3))/2 |
ln(abs(2*x+6))/2+c |
[x, NOCONST, FO RMAL] |
1 | ATInt_EqFormalDiff. | ||

Int | ! | ln(abs(x+3))/2 |
ln(abs(2*x+6))/2+c |
[x, NOCONST] |
-3 | ATInt_EqFormalDiff. | |

Int | -log(sqrt(x^2-4*x+3)+x-2)/2+(x *sqrt(x^2-4*x+3))/2-sqrt(x^2-4 *x+3)+c |
integrate(sqrt(x^2-4*x+3),x) |
x |
0 | ATInt_EqFormalDiff. | ||

Int | -log(sqrt(x^2-4*x+3)+x-2)/2+(x *sqrt(x^2-4*x+3))/2-sqrt(x^2-4 *x+3)+c |
integrate(sqrt(x^2-4*x+3),x) |
[x, FORMAL] |
1 | ATInt_EqFormalDiff. | ||

Irreducible quadratic | |||||||

Int | ln(x^2+7*x+7) |
ln(x^2+7*x+7) |
[x,NOCONST] |
1 | ATInt_const_condone. | ||

Int | ln(x^2+7*x+7) |
ln(abs(x^2+7*x+7)) |
[x,NOCONST] |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | ln(x^2+7*x+7)+c |
ln(x^2+7*x+7)+c |
x |
1 | ATInt_true_equiv. | ||

Int | ln(k*(x^2+7*x+7)) |
ln(x^2+7*x+7)+c |
x |
1 | ATInt_true_equiv. | ||

Int | ln(x^2+7*x+7) |
ln(abs(x^2+7*x+7))+c |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | ln(x^2+7*x+7)+c |
ln(abs(x^2+7*x+7))+c |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | -2*log(x)-(10*x^6)/3+x^3/3+5*l og(x^4)+c |
-2*log(abs(x))+(10*x^6)/3-x^3/ 3-5/x^3+c |
x |
0 | ATInt_generic. ATInt_logabs. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[20\\cdot x^5-x^2-\\frac{2}{x}+\\frac{15}{x^4}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[-20\\cdot x^5+x^2+\\frac{18}{x}\\] so you must have done something wrong! Your teacher may expect you to use the result \\(\\int\\frac{1}{x} dx = \\log(|x|)+c\\), rather than \\(\\int\\frac{1}{x} dx = \\log(x)+c\\). Please ask your teacher about this. | |||||||

Int | ln(abs(x^2+7*x+7))+c |
ln(abs(x^2+7*x+7))+c |
x |
1 | ATInt_true_equiv. | ||

Int | ln(k*abs(x^2+7*x+7)) |
ln(abs(x^2+7*x+7))+c |
x |
1 | ATInt_true_equiv. | ||

Two logs | |||||||

Int | log(abs(x-3))+log(abs(x+3)) |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | log(abs(x-3))+log(abs(x+3))+c |
log(abs(x-3))+log(abs(x+3)) |
x |
1 | ATInt_true_equiv. | ||

Int | log(abs(x-3))+log(abs(x+3)) |
log(x-3)+log(x+3) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | log(abs(x-3))+log(abs(x+3))+c |
log(x-3)+log(x+3) |
x |
1 | ATInt_true_equiv. | ||

Int | log(x-3)+log(x+3) |
log(x-3)+log(x+3) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | log(x-3)+log(x+3)+c |
log(x-3)+log(x+3) |
x |
1 | ATInt_true_equiv. | ||

Int | log(x-3)+log(x+3) |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | log(x-3)+log(x+3)+c |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | log(abs((x-3)*(x+3)))+c |
log(abs(x-3))+log(abs(x+3)) |
x |
1 | ATInt_true_equiv. | ||

Int | log(abs((x^2-9)))+c |
log(abs(x-3))+log(abs(x+3)) |
x |
0 | ATInt_EqFormalDiff. | ||

Int | 2*log(abs(x-2))-log(abs(x+2))+ (x^2+4*x)/2 |
-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | -log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
x |
1 | ATInt_true_equiv. | ||

Int | -log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2+c |
-log((x+2))+2*log((x-2))+(x^2+ 4*x)/2 |
x |
1 | ATInt_true_equiv. | ||

Inconsistent log(abs()) | |||||||

Int | log(abs(x-3))+log((x+3))+c |
log(x-3)+log(x+3) |
x |
0 | ATInt_true_equiv. ATInt_logabs_inconsistent. | ||

There appear to be strange inconsistencies between your use of \\(\\log(...)\\) and \\(\\log(|...|)\\). Please ask your teacher about this. | |||||||

Int | log((v-3))+log(abs(v+3))+c |
log(v-3)+log(v+3) |
v |
0 | ATInt_true_equiv. ATInt_logabs_inconsistent. | ||

There appear to be strange inconsistencies between your use of \\(\\log(...)\\) and \\(\\log(|...|)\\). Please ask your teacher about this. | |||||||

Int | log((x-3))+log(abs(x+3)) |
log(x-3)+log(x+3) |
x |
0 | ATInt_const. ATInt_logabs_inconsistent. | ||

There appear to be strange inconsistencies between your use of \\(\\log(...)\\) and \\(\\log(|...|)\\). Please ask your teacher about this. | |||||||

Int | 2*log((x-2))-log(abs(x+2))+(x^ 2+4*x)/2 |
-log(abs(x+2))+2*log(abs(x-2)) +(x^2+4*x)/2 |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. ATInt_logabs_inconsistent. | ||

Significant integration constant differences | |||||||

Int | 2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
t |
1 | ATInt_true_equiv. | ||

Int | 2*(sqrt(t))-10*log((sqrt(t)-5) )+c |
2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
t |
1 | ATInt_true_differentconst. | ||

Int | 2*(sqrt(t)-5)-10*log((sqrt(t)- 5))+c |
2*(sqrt(t)-5)-10*log(abs(sqrt( t)-5))+c |
t |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | 2*(sqrt(t))-10*log(abs(sqrt(t) -5))+c |
2*(sqrt(t)-5)-10*log(abs(sqrt( t)-5))+c |
t |
1 | ATInt_true_differentconst. | ||

Trig | |||||||

Int | 2*sin(x)*cos(x) |
sin(2*x)+c |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | 2*sin(x)*cos(x)+k |
sin(2*x)+c |
x |
1 | ATInt_true. | ||

Int | -2*cos(3*x)/3-3*cos(2*x)/2 |
-2*cos(3*x)/3-3*cos(2*x)/2+c |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | -2*cos(3*x)/3-3*cos(2*x)/2+1 |
-2*cos(3*x)/3-3*cos(2*x)/2+c |
x |
0 | ATInt_const_int. | ||

You need to add a constant of integration. This should be an arbitrary constant, not a number. | |||||||

Int | -2*cos(3*x)/3-3*cos(2*x)/2+c |
-2*cos(3*x)/3-3*cos(2*x)/2+c |
x |
1 | ATInt_true. | ||

Int | (tan(2*t)-2*t)/2 |
-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1) |
t |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | (tan(2*t)-2*t)/2+1 |
-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1) |
t |
0 | ATInt_const_int. | ||

You need to add a constant of integration. This should be an arbitrary constant, not a number. | |||||||

Int | (tan(2*t)-2*t)/2+c |
-(t*sin(4*t)^2-sin(4*t)+t*cos( 4*t)^2+2*t*cos(4*t)+t)/(sin(4* t)^2+cos(4*t)^2+2*cos(4*t)+1) |
t |
1 | ATInt_true. | ||

Int | tan(x)-x+c |
tan(x)-x |
x |
1 | ATInt_true. | ||

Int | 4*x*cos(x^12/%pi)+c |
x*cos(x^12/%pi)+c |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\cos \\left( \\frac{x^{12}}{\\pi} \\right)-\\frac{12\\cdot x^{12}\\cdot \\sin \\left( \\frac{x^{12}}{\\pi} \\right)}{\\pi}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[4\\cdot \\cos \\left( \\frac{x^{12}}{\\pi} \\right)-\\frac{48\\cdot x^{12} \\cdot \\sin \\left( \\frac{x^{12}}{\\pi} \\right)}{\\pi}\\] so you must have done something wrong! | |||||||

Int | 4*x*cos(x^50/%pi)+c |
x*cos(x^12/%pi)+c |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\cos \\left( \\frac{x^{12}}{\\pi} \\right)-\\frac{12\\cdot x^{12}\\cdot \\sin \\left( \\frac{x^{12}}{\\pi} \\right)}{\\pi}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[4\\cdot \\cos \\left( \\frac{x^{50}}{\\pi} \\right)-\\frac{200\\cdot x^{50} \\cdot \\sin \\left( \\frac{x^{50}}{\\pi} \\right)}{\\pi}\\] so you must have done something wrong! | |||||||

Note the difference in feedback here, generated by the options. | |||||||

Int | ((5*%e^7*x-%e^7)*%e^(5*x)) |
((5*%e^7*x-%e^7)*%e^(5*x))/25+ c |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\frac{e^{5\\cdot x+7}}{5}+\\frac{\\left(5\\cdot e^7\\cdot x-e^7\\right) \\cdot e^{5\\cdot x}}{5}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[5\\cdot e^{5\\cdot x+7}+5\\cdot \\left(5\\cdot e^7\\cdot x-e^7\\right) \\cdot e^{5\\cdot x}\\] so you must have done something wrong! | |||||||

Int | ((5*%e^7*x-%e^7)*%e^(5*x)) |
((5*%e^7*x-%e^7)*%e^(5*x))/25+ c |
[x,x*%e^(5*x+7) ] |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[x\\cdot e^{5\\cdot x+7}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[5\\cdot e^{5\\cdot x+7}+5\\cdot \\left(5\\cdot e^7\\cdot x-e^7\\right) \\cdot e^{5\\cdot x}\\] so you must have done something wrong! | |||||||

Inverse hyperbolic integrals | |||||||

Int | log(x-3)/6-log(x+3)/6+c |
log(x-3)/6-log(x+3)/6 |
x |
1 | ATInt_true_equiv. | ||

Int | asinh(x) |
ln(x+sqrt(x^2+1)) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | asinh(x)+c |
ln(x+sqrt(x^2+1)) |
x |
1 | ATInt_true. | ||

Int | -acoth(x/3)/3 |
log(x-3)/6-log(x+3)/6 |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | -acoth(x/3)/3 |
log(x-3)/6-log(x+3)/6 |
[x, NOCONST] |
1 | ATInt_true. | ||

Int | -acoth(x/3)/3+c |
log(x-3)/6-log(x+3)/6 |
x |
1 | ATInt_true. | ||

Int | -acoth(x/3)/3+c |
log(abs(x-3))/6-log(abs(x+3))/ 6 |
x |
1 | ATInt_true. | ||

Int | log(x-a)/(2*a)-log(x+a)/(2*a)+ c |
log(x-a)/(2*a)-log(x+a)/(2*a) |
x |
1 | ATInt_true_equiv. | ||

Int | -acoth(x/a)/a+c |
log(x-a)/(2*a)-log(x+a)/(2*a) |
x |
1 | ATInt_true. | ||

Int | -acoth(x/a)/a+c |
log(abs(x-a))/(2*a)-log(abs(x+ a))/(2*a) |
x |
1 | ATInt_true. | ||

Int | log(x-a)/(2*a)-log(x+a)/(2*a)+ c |
log(abs(x-a))/(2*a)-log(abs(x+ a))/(2*a) |
x |
0 | ATInt_EqFormalDiff. ATInt_logabs. | ||

Int | log(x-3)/6-log(x+3)/6+c |
-acoth(x/3)/3 |
x |
1 | ATInt_true. | ||

Int | log(abs(x-3))/6-log(abs(x+3))/ 6+c |
-acoth(x/3)/3 |
x |
1 | ATInt_true. | ||

Int | log(x-3)/6-log(x+3)/6 |
-acoth(x/3)/3 |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | atan(2*x-3)+c |
atan(2*x-3) |
x |
1 | ATInt_true. | ||

Int | atan((x-2)/(x-1))+c |
atan(2*x-3) |
x |
1 | ATInt_true. | ||

Int | atan((x-2)/(x-1)) |
atan(2*x-3) |
x |
0 | ATInt_const. | ||

You need to add a constant of integration, otherwise this appears to be correct. Well done. | |||||||

Int | atan((x-1)/(x-2)) |
atan(2*x-3) |
x |
0 | ATInt_generic. | ||

The derivative of your answer should be equal to the expression that you were asked to integrate, that was: \\[\\frac{2}{{\\left(2\\cdot x-3\\right)}^2+1}\\] In fact, the derivative of your answer, with respect to \\(x\\) is: \\[\\frac{\\frac{1}{x-2}-\\frac{x-1}{{\\left(x-2\\right)}^2}}{\\frac{{\\left( x-1\\right)}^2}{{\\left(x-2\\right)}^2}+1}\\] so you must have done something wrong! | |||||||

Stoutemyer (currently fails) | |||||||

Int | ! | 2/3*sqrt(3)*(atan(sin(x)/(sqrt (3)*(cos(x)+1)))-(atan(sin(x)/ (cos(x)+1))))+x/sqrt(3) |
2*atan(sin(x)/(sqrt(3)*(cos(x) +1)))/sqrt(3) |
x |
-3 | ATInt_const. | |

You need to add a constant of integration, otherwise this appears to be correct. Well done. |

Documentation home | Category index | Site map

The STACK documentation is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.