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Integrals
Question | Answer |
---|---|
u dv | uv + int v du |
F(f(x)) | int F(x)/f'(x) dx |
1/x | ln|x| +C |
a^x | a^x / (ln(a)) +C |
sin(x) | -cos(x) +C |
cos(x) | sin(x) +C |
tan(x) | ln(sec(x)) +C |
cot(x) | ln(sin(x)) +C |
sec(x) | ln(sec(x) + tan(x)) +C = ln(tan(u/2 + pi/4)) +C |
csc(x) | ln(tan(x/2)) +C |
sec^2(x) | tan(x) +C |
csc^2(x) | -cot(x) +C |
tan^2(x) | tan(x)-x +C |
cot^2(x) | -cot(x)-x +C |
sin^2(x) | 1/2(x-sin(x)cos(x)) +C |
cos^2(x) | 1/2(x+sin(x)cos(x)) +C |
sec(x)tan(x) | sec(x) +C |
csc(x)cot(x) | -csc(x) +C |
1/(x^2 + a^2) | tan^-1(x/a)/a +C |
1/(x^2 - a^2) | ln((x-a)/(x+a))/2a +C |
1/sqrt(a^2 - x^2) | sin^-1(x/a) +C |
1/sqrt(x^2 + a^2) | ln(x + sqrt(x^2 + a^2)) +C |
1/sqrt(x^2 - a^2) | ln(x + sqrt(x^2 - a^2)) +C |
1/(x sqrt(x^2 - a^2)) | 1/(a sec|x/a|) +C |
1/(x sqrt(x^2 + a^2)) | -ln((a + sqrt(x^2 + a^2))/x)/a |
1/(x sqrt(x^2 - a^2)) | -ln((a + sqrt(x^2 - a^2))/x)/a |
x e^x | x e^x - e^x +C |