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

The integral of sqrt(x)*x is 2/5 x^{5/2}+C

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integral of sqrt(x)*x

\int x \cdot x d x

\frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int x x d x

Simplify

x x : x^{\frac{3}{2}}

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

Apply the Power Rule

= \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} + C