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Mathematics LibreTexts

Table of Integrals

This page is a draft and is under active development. 

( \newcommand{\kernel}{\mathrm{null}\,}\)

Integration Rules

(Af(x)+Bg(x)dx=Af(x)dx+Bg(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)
ddxxaf(t)dt=f(x)

Integrals for Elementary Trancendental Functions

xndx=1n+1xn+1+C, if n1
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
dxa2x2=sin1(xa)+C(a>0,|x|<a)
dxa2+x2=1atan1(xa)+C(a>0)
dxa2x2=12aln|x+axa|+C(a>0)
dxxx2a2=1asec1|xa|+C(a>0,|x|>a)

Table of Integrals is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.

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