Question
Evaluate the following integrals:
$\int\frac{\log\text{x}}{\text{x}}\text{dx}$
$\int\frac{\log\text{x}}{\text{x}}\text{dx}$
✓
Answer
$\int\frac{\log\text{x}}{\text{x}}\text{dx}$
$\text{Let},\log\text{x}=\text{t}$
$\Rightarrow\frac{1}{\text{x}}=\frac{\text{dt}}{\text{dx}}$
$\text{Now},\int\frac{\log\text{x}}{\text{x}}\text{dx}$
$=\int\text{t}\text{dt}$
$=\frac{\text{t}^2}{2}+\text{C}=\frac{(\log\text{x})^2}{2}+\text{C}$
$\text{Let},\log\text{x}=\text{t}$
$\Rightarrow\frac{1}{\text{x}}=\frac{\text{dt}}{\text{dx}}$
$\text{Now},\int\frac{\log\text{x}}{\text{x}}\text{dx}$
$=\int\text{t}\text{dt}$
$=\frac{\text{t}^2}{2}+\text{C}=\frac{(\log\text{x})^2}{2}+\text{C}$
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