Question

solve
$\int e^x\frac{2+x}{(3+x{)}^2}dx$.

Answer 1

We have,

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

$\begin{array}{c}=\int e^x\left[\frac{\left(3+x\right)-1}{{\left(3+x\right)}^2}\right]dx\\ =\int e^x\left[\frac{1}{3+x}-\frac{1}{{\left(3+x\right)}^2}\right]dx\\ =\frac{e^x}{3+x}+C\end{array}$