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Parametric Differentiation

Evaluate : ...

Question

Evaluate : $\int [e^{(2 + 5 x)} + \frac{2}{6 x + 1}] d x$

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Solution

Let $I = \int e^{5 x + 2} + \frac{2}{6 x + 1} d x$

$= \int e^{5 x + 2} d x + \int \frac{2}{6 x + 1} d x$

$= \frac{1}{5} e^{5 x + 2} + \frac{2}{6} 1 n | 6 x + 1 |$

$I = \frac{1}{5} e^{5 x + 2} + \frac{1}{3} 1 n | 6 x + 1 |$

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