Table

Table of Integrals
$\int \, dx=x+C$	$\int \sec x\tan x\,dx=\sec x+C$
$\int x^{a }\, dx=\dfrac{x^{a +1}}{a +1}+C;$ $a \neq -1$	$\int \csc x\cot x\,dx=-\csc x+C$
$\int x^{-1}\, dx=\int \dfrac{1}{x}\, dx=\ln \vert x\vert +C$	$\int \csc ^{2}x\,dx=-\cot x+C$
$\int e^{x}\, dx=e^{x}+C$	$\int \dfrac{1}{\sqrt{1-x^{2}}} dx=$ $\sin^{-1}x+C$ , $\vert x\vert \lt1$
$\int a^{x}\, dx=\dfrac{a^{x}}{\ln a}+C;$ $a>0,$ $a\neq 1$	$\int \dfrac{1}{1+x^{2}}\, dx=\tan ^{-1}x+C$
$\int \sin x\,dx=-\cos x+C$	$\int \dfrac{1}{x\sqrt{x^{2}-1}}\, dx=\sec ^{-1}x+C\,$ , $\vert x\vert >1$
$\int \cos x\,dx=\sin x+C$	$\int \sinh x\,dx=\cosh x+C\,$
$\int \sec ^{2}x\,dx=\tan x+C$	$\int \cosh x\,dx=\sinh x+C$