# 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.

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