Question

Evaluate:

$\int {(\sqrt{x}-\frac{1}{\sqrt{x}})}^{2}dx$.

Answer 1

$\begin{array}{c}\int \begin{array}{c}{\left(\frac{x-1}{\sqrt{x}}\right)}^{2}dx\end{array}\\ \int {\left(\sqrt{x}\right)}^2-2\sqrt{x}.\frac{1}{\sqrt{x}}+{\left(\frac{1}{\sqrt{x}}\right)}^{2}dx\\ \int xdx-2\int dx+\int \frac{1}{x}dx\\ \frac{x^2}{2}-2x+\log x+c\end{array}$