Solve the integral $\int \frac{e^{2x}(2x+1)}{(x+1)^2}$ can you help me with this excercises: 
$$\int \frac{e^{2x}(2x+1)}{(x+1)^2}$$
I  can not get to the answer book:
the answer is $$\frac{e^{2x}}{x+1}$$
How?

Substitute $u=x+1$, you obtain $$\class{steps-node}{\cssId{steps-node-1}{\mathrm{e}^{-2}}}{\displaystyle\int}\dfrac{\left(2u-1\right)\mathrm{e}^{2u}}{u^2}\,\mathrm{d}u$$
Then use linearity of the integral and integrate by part the term $\frac{e^{2u}}{u^2}$. 
$$\int \frac{e^{2u}}{u^2}=\frac{e^{2u}}{u}-\int\frac{2ue^{2u}}{u^2}du$$
Finally :
$$\class{steps-node}{\cssId{steps-node-1}{\mathrm{e}^{-2}}}{\displaystyle\int}\dfrac{\left(2u-1\right)\mathrm{e}^{2u}}{u^2}\,\mathrm{d}u=\frac{e^{2u-2}}{u}$$
$u=x+1$ so $$\frac{e^{2u-2}}{u}=\frac{e^{2x}}{x+1}$$
