Question Index: Reduction Formulae

Reduction Formulae

Involving Trigonometric Functions

\displaystyle \int \sin^n {x} \,\mathrm{d}x
\displaystyle \int \cos^n {x} \,\mathrm{d}x
\displaystyle \int \tan^n {x} \,\mathrm{d}x
\displaystyle \int \sec^n {x} \,\mathrm{d}x
\displaystyle \int \sin^n {ax} \cdot \cos^m {ax} \,\mathrm{d}x
\displaystyle \int \sin^n {ax} \cdot \cos^m {ax} \,\mathrm{d}x

Involving Natural Log

\displaystyle \int (\ln {x})^n \,\mathrm{d}x
\displaystyle \int x^{m}\cdot(\ln {x})^n \,\mathrm{d}x

Miscellaneous

\displaystyle \int x^n \cdot \cos {x} \,\mathrm{d}x
\displaystyle \int x^n \cdot e^{ax} \,\mathrm{d}x
\displaystyle \int \frac{x^2}{(a^2+x^2)^n} \,\mathrm{d}x

 

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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