Table of Integrals
This page is a draft and is under active development.
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Integration Rules
∫(Af(x)+Bg(x)dx=A∫f(x)dx+B∫g(x)dx |
∫f′(g(x))g′(x)dx=f(g(x))+C |
∫U(x)dV(x)=U(x)V(x)−∫V(x)dU(x) |
∫baf′(x)dx=f(b)−f(a) |
ddx∫xaf(t)dt=f(x) |
Integrals for Elementary Trancendental Functions
∫xndx=1n+1xn+1+C, if n≠−1 |
∫dxx=ln|x|+C |
∫exdx=ex+C |
∫ax=axln(a)+C |
∫sin(x)dx=−cos(x)+C |
∫cos(x)dx=sin(x)+C |
∫sec2(x)dx=tan(x)+C |
∫csc2(x)dx=−cot(x)+C |
∫sec(x)tan(x)dx=sec(x)+C |
∫csc(x)cot(x)dx=−csc(x)+C |
∫tan(x)dx=ln|sec(x)|+C |
∫cot(x)dx=ln|sin(x)|+C |
∫sec(x)dx=ln|sec(x)+tan(x)|+C |
∫csc(x)dx=ln|csc(x)−cot(x)|+C |
∫dx√a2−x2=sin−1(xa)+C(a>0,|x|<a) |
∫dxa2+x2=1atan−1(xa)+C(a>0) |
∫dxa2−x2=12aln|x+ax−a|+C(a>0) |
∫dxx√x2−a2=1asec−1|xa|+C(a>0,|x|>a) |