The following integral
$$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (2 cosec x)^{17} dx $$
is equal to

A

$$\int_{0}^{\log (1 + \sqrt 2)}2 (e^u + e^{-u})^{16} du $$

B

$$\int_{0}^{\log (1 + \sqrt 2)} (e^u + e^{-u})^{17} du $$

C

$$\int_{0}^{\log (1 + \sqrt 2)}2 (e^u - e^{-u})^{17} du $$

D

$$\int_{0}^{\log (1 + \sqrt 2)}2 (e^u - e^{-u})^{16} du $$