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

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

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integral of (e^x+sqrt(x))

\int (e^{x} + x) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (3^{4 x + 5})

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

\frac{d}{d x} (\frac{1}{10} x - \frac{1}{4})

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

2 - 2 cos^{2} (x)

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