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

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

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

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

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

Solution steps

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

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

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