What is the integral of sec^2(x)+e^{2x} ?

The integral of sec^2(x)+e^{2x} is tan(x)+1/2 e^{2x}+C

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integral of sec^2(x)+e^{2x}

\int sec^{2} (x) + e^{2 x} d x

tan (x) + \frac{1}{2} e^{2 x} + C

Solution steps

\int sec^{2} (x) + e^{2 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sec^{2} (x) d x + \int e^{2 x} d x

\int sec^{2} (x) d x = tan (x)

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

= tan (x) + \frac{1}{2} e^{2 x}

Add a constant to the solution

= tan (x) + \frac{1}{2} e^{2 x} + C

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What is the integral of sec^2(x)+e^{2x} ?
The integral of sec^2(x)+e^{2x} is tan(x)+1/2 e^{2x}+C