Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises - Page 354: 108

$\ln|\csc(e^{2x})+\cot(e^{2x})|)+C$

$\int e^{2x} csc(e^{2x})dx$ let $e^{2x}=u$ $2e^{2x}dx=du$ $\int e^{2x} csc(e^{2x})dx$ $=\frac{1}{2}\int csc(u)du$ $=\frac{1}{2}(-ln|csc(u)+cot(u)|)+C$ $=\frac{1}{2}(-ln|csc(e^{2x})+cot(e^{2x})|)+C$