What is the integral of (e^{3x}+5) ?

The integral of (e^{3x}+5) is 1/3 e^{3x}+5x+C

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integral of (e^{3x}+5)

\int (e^{3 x} + 5) d x

\frac{1}{3} e^{3 x} + 5 x + C

Solution steps

\int e^{3 x} + 5 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^{3 x} d x + \int 5 d x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

\int 5 d x = 5 x

= \frac{1}{3} e^{3 x} + 5 x

Add a constant to the solution

= \frac{1}{3} e^{3 x} + 5 x + C

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What is the integral of (e^{3x}+5) ?
The integral of (e^{3x}+5) is 1/3 e^{3x}+5x+C