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

The integral of sqrt(x)+e^{2x} is 2/3 x^{3/2}+1/2 e^{2x}+C

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integral of sqrt(x)+e^{2x}

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

\frac{2}{3} x^{\frac{3}{2}} + \frac{1}{2} e^{2 x} + C

Solution steps

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

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

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

= \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{2} e^{2 x}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{2} e^{2 x} + C

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What is the integral of sqrt(x)+e^{2x} ?
The integral of sqrt(x)+e^{2x} is 2/3 x^{3/2}+1/2 e^{2x}+C