Evaluate: 5^x 3^x d x - Vidyadip

Question

Evaluate: $\int \frac{5^x}{3^x} d x$

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Answer

$I=\int \frac{5^x}{3^x} d x=\int\left(\frac{5}{3}\right)^x d x$
$\therefore \quad I=\frac{\left(\frac{5}{3}\right)^x}{\log \left(\frac{5}{3}\right)}+c \quad \ldots \ldots .\left[\int a^x d x=\frac{a^x}{\log a}+c, \quad\right.$ where $\left.a \neq 0, a>0\right]$

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