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

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

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integral of x*sqrt(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}}

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

Add a constant to the solution

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

\frac{1}{x - 1}

x \cdot y^{^{'}} = x^{2} - 2 x y - y^{2} + y

\int 3 x 2 x^{2} + 1 d x

\frac{\partial}{\partial y} (4 z e^{x yz})

x \to - 9 - lim (\frac{- 6 x}{x + 9})