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find-f-a-0-pi-8-ln-1-a-sin-d-with-o-lt-a-lt-1-




Question Number 113629 by mathmax by abdo last updated on 14/Sep/20
find f(a) =∫_0 ^(π/8)  ln(1+a sinθ)dθ   with o<a<1
$$\mathrm{find}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{8}}} \:\mathrm{ln}\left(\mathrm{1}+\mathrm{a}\:\mathrm{sin}\theta\right)\mathrm{d}\theta\:\:\:\mathrm{with}\:\mathrm{o}<\mathrm{a}<\mathrm{1} \\ $$

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