$\int (s e c^{2} x + e^{x} + e^{3 x}) d x$ is equals to

sec x + tan x + e^{x} + e^{3 x} + C

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tan x + e^{x} + e^{3 x} + C

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tan x + e^{x} + \frac{e^{3 x}}{3} + C

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sec x + e^{x} + \frac{e^{3 x}}{3} + C

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Solution

The correct option is C $tan x + e^{x} + \frac{e^{3 x}}{3} + C$
$\int (s e c^{2} x + e^{x} + e^{3 x}) d x$
= $\int s e c^{2} x d x + \int e^{x} d x + \int e^{3 x} d x$
$tan x + e^{x} + \frac{e^{3 x}}{3} + C$

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