The integral is equal to:

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

The integral ∫π/4π/2(2csc⁡x)17 dx\int_{\pi/4}^{\pi/2}(2\csc x)^{17}\,dx is equal to: (1) ∫0log⁡(1+2)2(eu+e−u)16 du\int_{0}^{\log(1+\sqrt{2})}2(e^u+e^{-u})^{16}\,du (2) ∫0log⁡(1+2)(eu+e−u)17 du\int_{0}^{\log(1+\sqrt{2})}(e^u+e^{-u})^{17}\,du (3) ∫0log⁡(1+2)(eu−e−u)17 du\int_{0}^{\log(1+\sqrt{2})}(e^u-e^{-u})^{17}\,du (4) ∫0log⁡(1+2)2(eu−e−u)16 du\int_{0}^{\log(1+\sqrt{2})}2(e^u-e^{-u})^{16}\,du

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