Question

If In is the integral of 1/((1+x^2)^n), from 0 to 1.
How would you prove that 2n*I(n+1)=2^-n+(2n-1)In

Answer 1

\[I _{n}=\int\limits_{0}^{1}\frac{ 1 }{ (1+x ^{2})^{n} }dx\]

Answer 2

@kc_kennylau

Answer 3

@perl , aha, another helper online!!

Answer 4

use integration by part