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Question Number 188511 by universe last updated on 02/Mar/23

e v a l u a t e

\int_{0}^{π} \frac{d x}{a + b \cos x}, a > 0

a n d d e d u c e t h a t

\int_{0}^{π} \frac{d x}{{(a + b \cos x)}^{2}} = \frac{π a}{{(a^{2} - b^{2})}^{3 / 2}}; a^{2} > b^{2}

a n d \int_{0}^{π} \frac{\cos x d x}{{(a + b \cos x)}^{2}} = \frac{- π b}{{(a^{2} - b^{2})}^{3 / 2}}; a^{2} > b^{2}