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Integration Formulas

Rules of Integration and Integration of Trigonometric and Hyperbolic Functions

QuestionAnswer
∫1du u + c
∫adu au + c
∫au^n du a u^(n+1)/(n+1) + c, n =/= -1
∫1/u du ln|u| + c
∫e^u du e^u + c
∫a^u du a^u/ln(a) + c
∫ln(x) du xln(x) - x + c
∫sin(u) du -cos(u) + c
∫cos(u) du sin(u) + c
∫sec^2(u) du tan(u) + c
∫csc^2(u) du -cot(u) + c
∫sec(u)tan(u) du sec(u) + c
∫csc(u)cot(u) du -csc(u) + c
∫tan(u) du ln|sec(u)| + c -ln|cos(u)| + c
∫sec(u) du ln|tan(u) + sec(u)| + c
∫cot(u) du ln|sin(u)| + c
∫csc(u) du ln|csc(u) - cot(u)| + c -ln|cot(u) + csc(u)| + c
∫sinh(u) du cosh(u) + c
∫cosh(u) du sinh(u) + c
∫sech^2(u) du tanh(u) + c
∫csch^2(u) du -coth(u) + c
∫sech(u)tanh(u) du -sech(u) + c
∫csch(u)coth(u) du -csch(u) + c
∫1/sqrt(a^2 - u^2) du arcsin(u/a) + c
∫-1/sqrt(a^2 - u^2) du arccos(u/a) + c -arcsin(u/a) + c
∫1/(a^2 + u^2) du (1/a)arctan(u/a) + c
∫1/usqrt(u^2 - a^2) du (1/a)arcsec(u/a) + c
∫1/sqrt(a^2 + u^2) du arcsinh(u/a) + c ln(u + sqrt(u^2 + a^2) + c
∫1/sqrt(u^2 - a^2) du arccosh(u/a) + c ln|u + sqrt(u^2 - a^2) + c
∫1/(a^2 - u^2) du (1/2a)arctanh(u/a) + c (1/2a) ln|(a + u)/(a - u)| + c
∫1/usqrt(a^2 - u^2) du (-1/a)arcsech(u/a) + c (-1/a)ln|(a+sqrt(a^2 - u^2))/u| + c
∫1/usqrt(a^2 + u^2) du (-1/a)arccsch(u/a) + c (-1/a)ln|(a+sqrt(a^2 + u^2))/u| + c
Created by: jefranco1
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