Evaluate (1+ )^2 x dx - Vidyadip

Question

Evaluate $\int\frac{(1+\log\text{x})^2}{\text{x}}\text{ dx}$

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Answer

Let $\text{I}=\int\frac{(1+\log\text{x})^2}{\text{x}}\text{ dx}$
Let $1+\log\text{x}=\text{t}$
$\frac{1}{\text{x}}\text{dx}=\text{dt}$
$\text{I}=\int\text{t}^2\text{dt}$
$=\frac{\text{t}^3}{3}+\text{C}$
$\text{I}=\frac{(1+\log\text{x})^3}{3}+\text{C}$

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