Evaluate the following : 3^x-4^x 5^x d x - Vidyadip

Question

Evaluate the following : $\int \frac{3^x-4^x}{5^x} \cdot d x$

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Answer

$
\begin{aligned}
I & =\int\left(\frac{3^x}{5^x}-\frac{4^x}{5^x}\right) \cdot d x \\
& =\int\left[\left(\frac{3}{5}\right)^x-\left(\frac{4}{5}\right)^x\right] \cdot d x \\
& =\frac{\left(\frac{3}{5}\right)^x}{\log \frac{3}{5}}-\frac{\left(\frac{4}{5}\right)^x}{\log \frac{4}{5}}+c
\end{aligned}
$

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