Evaluate: 1 a^xb^x dx - Vidyadip

Question

Evaluate:
$\int\frac{1}{\text{a}^\text{x}\text{b}^\text{x}}\text{dx}$

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Answer

$\int\frac{1}{\text{a}^\text{x}\text{b}^\text{x}}\text{dx}=\int\text{a}^{-\text{x}}\text{b}^{-\text{x}}\text{dx}$
$=\int(\text{ab})^{-\text{x}}\text{dx}$
$=\frac{(\text{ab})^{-\text{x}}}{\log_\text{e}(\text{ab})^{-1}}+\text{c}$
$=\frac{(\text{ab})^{-\text{x}}}{-\log_\text{e}(\text{ab})}+\text{c}$
$=\frac{\text{a}^{-\text{x}}\text{b}^{-\text{x}}}{-\log_\text{e}(\text{ab})}+\text{c}$

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