Problem $1.(1$ point$)$

Evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-18e^x-60}{e^{2x}+8e^x+12}dx$

Answer:

$+C$

Hint: let $u=e^{x}so$ that $du=e^{x}dx$ and thus $dx=d\frac{u}{u}.$ This substitution converts the integrand into a rational function $inu,$ which can $be$ integrated after partial fraction decomposition.