The following integral ∫ (2 cosec x)^17 ; x ∈ π/4 , π/2 dx is equal to

Question

The following integral \(\int\limits_{\pi /4}^{\pi /2}\) (2 cosec x)¹⁷ dx is equal to

(A) \(\int\limits_{0}^{log(1+\sqrt{2})}\) 2(e^u + e^-u)¹⁶ du

(B) \(\int\limits_{0}^{log(1+\sqrt{2})}\) (e^u + e^-u)¹⁷ du

(C) \(\int\limits_{0}^{log(1+\sqrt{2})}\) (e^u - e^-u)¹⁷ du

(D) \(\int\limits_{0}^{log(1+\sqrt{2})}\) 2(e^u - e^-u)¹⁶ du

Answer 1

(A) \(\int\limits_{0}^{log(1+\sqrt{2})}\) 2(e^u + e^-u)¹⁶ du