Question Number 222245 by Nicholas666 last updated on 20/Jun/25
$$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\:\frac{\mathrm{cos}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{2}} \left({x}\right)\:\mathrm{cos}^{\mathrm{2}} \left({x}\right)}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \left({x}\right)}\right)\centerdot\mathrm{ln}\left(\frac{\mathrm{1}\:+\:\mathrm{sin}\left({x}\right)}{\mathrm{1}\:+\:\mathrm{cos}\left({x}\right)}\right)}{\:\sqrt{\mathrm{1}\:+\:\mathrm{cos}^{\mathrm{2}} \left({x}\right)\:−\:\mathrm{sin}^{\mathrm{2}} \left({x}\right)}}\:\:\mathrm{d}{x}\:\:\:\:\:\: \\ $$$$ \\ $$
Answered by MathematicalUser2357 last updated on 21/Jun/25
$$\mathrm{0} \\ $$
Commented by MathematicalUser2357 last updated on 21/Jun/25
$$…\mathrm{And}\:\mathrm{someone}\:\mathrm{said}\:\mathrm{that}\:\mathrm{question}\:\mathrm{may}\:\mathrm{came}\:\mathrm{from}\:\mathrm{the}\:\mathrm{book}. \\ $$
Answered by MrGaster last updated on 21/Jun/25
