$\int (e^{x} + e^{9 ln x} + e^{9 ln a}) d x$ is equal to (where $a > 0$ and $C$ is the constant of integration)

e^{x} + \frac{x^{10}}{10} + a^{9} x + C

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e^{x} + \frac{x^{10}}{10} - a^{9} x + C

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e^{x} - \frac{x^{10}}{10} + a^{9} x + C

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e^{x} - \frac{x^{10}}{10} + a^{9} x^{2} + C

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Solution

The correct option is A $e^{x} + \frac{x^{10}}{10} + a^{9} x + C$
$\int (e^{x} + e^{9 ln x} + e^{9 ln a}) d x {∵ e^{ln x} = x} = \int e^{x} d x + \int x^{9} d x + \int a^{9} d x = e^{x} + \frac{x^{9 + 1}}{9 + 1} + a^{9} x + C = e^{x} + \frac{x^{10}}{10} + a^{9} x + C$

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