What is the integral of 10e^{3x}+1 ?

The integral of 10e^{3x}+1 is 10/3 e^{3x}+x+C

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integral of 10e^{3x}+1

\int 10 e^{3 x} + 1 d x

\frac{10}{3} e^{3 x} + x + C

Solution steps

\int 10 e^{3 x} + 1 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 10 e^{3 x} d x + \int 1 d x

\int 10 e^{3 x} d x = \frac{10}{3} e^{3 x}

\int 1 d x = x

= \frac{10}{3} e^{3 x} + x

Add a constant to the solution

= \frac{10}{3} e^{3 x} + x + C

What is the integral of 10e^{3x}+1 ?
The integral of 10e^{3x}+1 is 10/3 e^{3x}+x+C