Chapter 8.5, Problem 81E

Preliminary steps The following integrals require a preliminary step such as a change of variables before using the method of partial fractions. Evaluate these integrals.

81. ${\displaystyle \int \frac{\left(e^{3x}+e^{2x}+e^x\right)}{{\left(e^{2x}+1\right)}^2}dx}$