Answer
$\displaystyle \frac{7}{2}+\ln 2$
Work Step by Step
$\displaystyle \int_{1}^{2}\frac{(x+1)^{2}}{x}dx=\int_{1}^{2}\frac{x^{2}+2x+1}{x}dx$
$=\displaystyle \int_{1}^{2}\left(x+2+\frac{1}{x}\right)dx$
$=\displaystyle \left[\frac{1}{2}x^{2}+2x+\ln|x|\right]_{1}^{2}$
$=(2+4+\displaystyle \ln 2)-\left(\frac{1}{2}+2+0\right)$
$=\displaystyle \frac{7}{2}+\ln 2$
