Evaluate x dx - Vidyadip

Question

Evaluate $\int\frac{\log\text{x}}{\text{x}}\text{ dx}$

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Answer

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

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