let f(x)=∫_0 ^(π/2) ln(((1−xsint)/(1+xsint)))dt . 1) find the value of I = ∫_0 ^(π/2) ln(1−xsint)dt and J = ∫_0 ^(π/2) ln(1+xsint)dt 2) find a simple form of f(x) 3) developp f at integr serie


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Question Number 40624 by math khazana by abdo last updated on 25/Jul/18

$l e t f (x) = \int_{0}^{\frac{π}{2}} l n (\frac{1 - x s i n t}{1 + x s i n t}) d t .$ $1) f i n d t h e v a l u e o f I = \int_{0}^{\frac{π}{2}} l n (1 - x s i n t) d t$ $a n d J = \int_{0}^{\frac{π}{2}} l n (1 + x s i n t) d t$ $2) f i n d a s i m p l e f o r m o f f (x)$ $3) d e v e l o p p f a t i n t e g r s e r i e$
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