What is the integral of (e^{2x}+3) ?

The integral of (e^{2x}+3) is 1/2 e^{2x}+3x+C

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integral of (e^{2x}+3)

\int (e^{2 x} + 3) d x

\frac{1}{2} e^{2 x} + 3 x + C

Solution steps

\int e^{2 x} + 3 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 e^{2 x} d x + \int 3 d x

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

\int 3 d x = 3 x

= \frac{1}{2} e^{2 x} + 3 x

Add a constant to the solution

= \frac{1}{2} e^{2 x} + 3 x + C

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What is the integral of (e^{2x}+3) ?
The integral of (e^{2x}+3) is 1/2 e^{2x}+3x+C