Find the following integrals in Exercises. ( x -1 x )^2 - Vidyadip

Question

Find the following integrals in Exercises. $\int\bigg(\sqrt{\text{x}}-\frac{1}{\sqrt{\text{x}}}\bigg)^2$

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Answer

$\int\bigg(\sqrt{\text{x}}-\frac{1}{\sqrt{\text{x}}}\bigg)^2\text{ dx}$
$=\int \bigg\{\big(\sqrt{\text{x } } \big)^2+\bigg(\frac{1}{\sqrt{\text{x}}}\bigg)^2-2\sqrt{\text{x}}\frac{1}{\sqrt{\text{x}}}\bigg\}\text{ dx}$
$ =\int\bigg(\text{x}+\frac{1}{\text{x}}-2\bigg)\text{ dx}$
$=\int\text{x}\text{ dx}+\int\frac{1}{\text{x}}\text{ dx}-\int 2\text{ dx}=\frac{\text{x}^2}{2}+\log\mid\text{x}\mid-2\text{x}+\text{c}$

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