I-n-0-pi-4-1-cos-2n-1-x-dx-Prove-by-parts-that-2nI-n-2n-1-I-n-1-2-n-2-

Question Number 167740 by LEKOUMA last updated on 24/Mar/22

I_{n} = \int_{0}^{\frac{π}{4}} \frac{1}{\cos^{2 n + 1} x} d x

P r o v e b y p a r t s t h a t :

2 {n I}_{n} = (2 n - 1) I_{n - 1} + \frac{2^{n}}{\sqrt{2}}