\(\int\limits^2_1 \frac{(x + 1)^3}{x^2}dx\)
\(= \int\limits^2_1 \left(x + 3 + \frac3x + \frac1{x^2}\right)dx\)
\(= \left(2 + 6 +3log2 - \frac12\right)- \left(\frac12 + 3+ 3log1-1\right)\)
\(= 8 + 3log2 - \frac12 - \frac12 - 2\) \((\because log 1 = 0)\)
\(= 5 + 3log2\)