Evaluate: e^ x x dx - Vidyadip

Question

Evaluate:
$\int\frac{\text{e}^{\log\sqrt{\text{x}}}}{\text{x}}\text{dx}$

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Answer

$\int\frac{\text{e}^{\log\sqrt{\text{x}}}}{\text{x}}\text{dx}=\int\frac{\sqrt{\text{x}}}{\text{x}}\text{dx}$
$=\int\text{x}^\frac{1}{2}\times\text{x}^{-1}\text{dx}$
$=\int\text{x}^{\frac{1}{2}-1}\text{dx}$
$=\int\frac{\text{x}^{\frac{-1}{2}+1}+\text{c}}{\frac{-1}{2}+1}$
$=\frac{\text{x}^\frac{1}{2}}{\frac{1}{2}}$
$=\sqrt{\text{x}}+\text{c}$

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