$\int (e^{2 x} + x^{3} + sin x) d x$ is equal to
(where $C$ is constant of integration)

e^{2 x} + \frac{x^{4}}{4} - sin x + C

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\frac{e^{2 x}}{2} + \frac{x^{4}}{3} + cos x + C

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\frac{e^{2 x}}{2} + \frac{x^{4}}{4} - cos x + C

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\frac{e^{2 x}}{2} + \frac{x^{4}}{4} + cos x + C

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Solution

The correct option is C $\frac{e^{2 x}}{2} + \frac{x^{4}}{4} - cos x + C$
$\int (e^{2 x} + x^{3} + sin x) d x = \int e^{2 x} d x + \int x^{3} d x + \int sin x d x$
$= \frac{e^{2 x}}{2} + \frac{x^{4}}{4} - cos x + C$

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