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

The integral of (3x^{2/3}+2e^x) is 9/5 x^{5/3}+2e^x+C

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

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

\frac{9}{5} x^{\frac{5}{3}} + 2 e^{x} + C

Solution steps

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

\int 3 x^{\frac{2}{3}} d x = \frac{9}{5} x^{\frac{5}{3}}

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

= \frac{9}{5} x^{\frac{5}{3}} + 2 e^{x}

Add a constant to the solution

= \frac{9}{5} x^{\frac{5}{3}} + 2 e^{x} + C

What is the integral of (3x^{2/3}+2e^x) ?
The integral of (3x^{2/3}+2e^x) is 9/5 x^{5/3}+2e^x+C