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Problem The integral ∫ π / 4 π / 2 ( 2 csc x ) 17 d x \int_{\pi/4}^{\pi/2} (2 \csc x)^{17} \, dx ∫ π /4 π /2 ( 2 csc x ) 17 d x is equal to:
a. ∫ 0 log ( 1 + 2 ) 2 ( e u + e − u ) 16 d u \int_{0}^{\log(1+\sqrt{2})} 2(e^u + e^{-u})^{16} du ∫ 0 l o g ( 1 + 2 ) 2 ( e u + e − u ) 16 d u
b. ∫ 0 log ( 1 + 2 ) ( e u + e − u ) 17 d u \int_{0}^{\log(1+\sqrt{2})} (e^u + e^{-u})^{17} du ∫ 0 l o g ( 1 + 2 ) ( e u + e − u ) 17 d u
c. ∫ 0 log ( 1 + 2 ) ( e u − e − u ) 17 d u \int_{0}^{\log(1+\sqrt{2})} (e^u - e^{-u})^{17} du ∫ 0 l o g ( 1 + 2 ) ( e u − e − u ) 17 d u
d. ∫ 0 log ( 1 + 2 ) 2 ( e u − e − u ) 16 d u \int_{0}^{\log(1+\sqrt{2})} 2(e^u - e^{-u})^{16} du ∫ 0 l o g ( 1 + 2 ) 2 ( e u − e − u ) 16 d u
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