JEE Main 20241 Feb, Morning shiftMathematicsMediumIntegral Calculus369× since 2002If ∫−π/2π/282cosx dx(1+esinx)(1+sin4x)=απ+βloge(3+22)\int\limits_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x \mathrm{~d} x}{\left(1+\mathrm{e}^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _{\mathrm{e}}(3+2 \sqrt{2})−π/2∫π/2(1+esinx)(1+sin4x)82cosx dx=απ+βloge(3+22), where α,β\alpha, \betaα,β are integers, then α2+β2\alpha^2+\beta^2α2+β2 equals :Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
