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The following integral $$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (2 cosec x)^{17} dx $$is equal to
$$\int_{0}^{\log (1 + \sqrt 2)}2 (e^u + e^{-u})^{16} du $$
$$\int_{0}^{\log (1 + \sqrt 2)} (e^u + e^{-u})^{17} du $$
$$\int_{0}^{\log (1 + \sqrt 2)}2 (e^u - e^{-u})^{17} du $$
$$\int_{0}^{\log (1 + \sqrt 2)}2 (e^u - e^{-u})^{16} du $$
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