Given that In = integral between 1 and 0 of 1/(1+x^2)^n, show that for n>1, 2(n-1)In = 2^(1-n) + (2n-3)In-1
Start from $\displaystyle I_{n-1} = \int_0^1\!\!\!1*(1+x^2)^{-(n-1)}dx$ and integrate by parts (integrating the 1 and differentiating the $\displaystyle (1+x^2)^{-(n-1)}$).