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

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

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integral of (x+sqrt(x))

\int (x + x) d x

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

Solution steps

\int 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 x d x + \int x d x

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

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

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

Add a constant to the solution

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

3 (x^{2} + 5 x)^{3}

\frac{d}{d x} (6 x \cdot sin (3 x^{2}))

\frac{d}{d x} (ln (\frac{4 - x}{4 + x}))

\int_{0}^{3} c (3 - x) d x

\int \frac{5 x - 3}{x + 1} d x

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