What is the integral of 2e^{x/3+4}+5 ?

The integral of 2e^{x/3+4}+5 is 6e^{4+x/3}+5x+C

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integral of 2e^{x/3+4}+5

\int 2 e^{\frac{x}{3} + 4} + 5 d x

6 e^{4 + \frac{x}{3}} + 5 x + C

Solution steps

\int 2 e^{\frac{x}{3} + 4} + 5 d x

e^{\frac{x}{3} + 4} = e^{4} e^{\frac{x}{3}}

= \int 2 e^{4} e^{\frac{x}{3}} + 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 2 e^{4} e^{\frac{x}{3}} d x + \int 5 d x

\int 2 e^{4} e^{\frac{x}{3}} d x = 6 e^{4 + \frac{x}{3}}

\int 5 d x = 5 x

= 6 e^{4 + \frac{x}{3}} + 5 x

Add a constant to the solution

= 6 e^{4 + \frac{x}{3}} + 5 x + C

What is the integral of 2e^{x/3+4}+5 ?
The integral of 2e^{x/3+4}+5 is 6e^{4+x/3}+5x+C