## Reduction formula doubt.

If In=∫(1a2+x2)ndx Prove that:In=x2a2(n−1)(a2+x2)(n−1)+2n−32(n−1)a2In−1 I used Ibp but couldn’t get such a relation. Please help me. Also, please do not use induction. Answer Hint: By parts, setting u=1(a2+x2)n−1, dv=dx, whence du=−2(n−1)x(a2+x2)ndx,v=x One obtains then In−1=x(a2+x2)n−1+2(n−1)∫x2(a2+x2)ndx Note that, writing x2=a2+x2−a2, the integral is equal to In−1−a2In. AttributionSource : Link , Question Author : Aditya Kumar , … Read more