Answer
$$\frac{7}{2} +\ln 2$$
Work Step by Step
Given $$\int_{1}^{2} \frac{(x+1)^{2}}{x} d x$$
Since
\begin{align*}
\int_{1}^{2} \frac{(x+1)^{2}}{x} d x&=\int_{1}^{2} \frac{ x^2+2x+1 }{x} d x\\
&=\int_{1}^{2} \left( x+2+\frac{1 }{x} \right)d x\\
&=\frac{1}{2}x^2+2x+\ln x\bigg|_{1}^2\\
&=\frac{3}{2} +2+\ln 2\\
&=\frac{7}{2} +\ln 2
\end{align*}
