Reduction Formula

{\LARGE Question:}

Derive the reduction formula below:

\displaystyle \int \frac{x^2}{(a^2+x^2)^n} \,dx = \frac {1} {2n-2} \left ( -\frac{x}{(a^2+x^2)^{n-1}} +\int \frac{1}{(a^2+x^2)^{n-1}} \,dx \right ) \,dx


{\LARGE Solution:}

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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