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