let give the function f(x)=∫_0 ^π ln(1+xcosθ)dθ with ∣x∣<1 1) find a simple form of f(x) 2)calculate ∫_0 ^π ln(1−cosθ)dθ 3)calculate ∫


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Question Number 31463 by abdo imad last updated on 08/Mar/18

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