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

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

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integral of 3e^{2x}+3

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

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

Solution steps

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

\int 3 e^{2 x} d x = \frac{3}{2} e^{2 x}

\int 3 d x = 3 x

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

Add a constant to the solution

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

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