If I_m = ( x + x)^m

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

I_m = \int (\sin x + \cos x)^m \, dx

, then show that

m I_m = (\sin x + \cos x)^{m-1} \cdot (\sin x - \cos x) + 2 (m-1) I_{m-2}