Integration Formulas

I have collected some of the most basic and important integration formulas here. These are the ones that you’ll get to use every day.

You can read it online or download the integration formulas PDF here.

$$ \int { { x }^{ n }dx=\frac { { x }^{ n+1 } }{ n+1 } +C } $$
$$ \int { { e }^{ x }dx={ e }^{ x }+C } $$
$$ \int { \frac { 1 }{ x } } dx=\ln { \left| x \right| } +C$$
$$ \int { \sin { x } dx=-\cos { x } +C } $$
$$ \int { \cos { x } dx=\sin { x } +C } $$
$$ \int { \sec ^{ 2 }{ x } } dx=\tan { x }+C$$
$$ \int { \csc ^{ 2 }{ x } } dx=-\cot { x } +C$$
$$ \int { \sec { x\tan { x } } } dx=\sec { x } +C$$
$$ \int { \csc { x } \cot { x } } dx=-\csc { x } +C$$
$$ \int { { \left( ax+b \right) }^{ n }dx=\frac { 1 }{ a } } \cdot \frac { { \left( ax+b \right) }^{ n+1 } }{ n+1 } +C$$
$$ \int { { e }^{ ax+b }dx=\frac { 1 }{ a } } \cdot { e }^{ ax+b }+C$$
$$ \int { \frac { 1 }{ ax+b } dx=\frac { 1 }{ a } } \cdot \ln { \left| ax+b \right| } +C$$
$$ \int { \sin { \left( ax+b \right) dx } } =-\frac { 1 }{ a } \cos { \left( ax+b \right) } +C$$
$$ \int { \cos { \left( ax+b \right) dx=\frac { 1 }{ a } } } \sin { \left( ax+b \right) +C } $$
$$ \int { \sec ^{ 2 }{ \left( ax+b \right) } } dx=\frac { 1 }{ a } \cdot \tan { \left( ax+b \right) +C } $$
$$ \int { \csc { \left( ax+b \right) \cot { \left( ax+b \right) dx } } } =-\frac { 1 }{ a } \cdot \csc { \left( ax+b \right) } +C$$
$$ \int { \csc ^{ 2 }{ \left( ax+b \right) } } dx=-\frac { 1 }{ a } \cdot \cot { \left( ax+b \right) +C } $$
$$ \int { \sec { \left( ax+b \right) \tan { \left( ax+b \right) } dx= } } \frac { 1 }{ a } \cdot \sec { \left( ax+b \right) +C } $$