What is the integral of sqrt(x)*x^2 ?

The integral of sqrt(x)*x^2 is 2/7 x^{7/2}+C

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integral of sqrt(x)*x^2

integral

x \cdot x^{2}

\frac{2}{7} x^{\frac{7}{2}} + C

Solution steps

\int x x^{2} d x

Simplify

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

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

Apply the Power Rule

: \frac{2}{7} x^{\frac{7}{2}}

= \frac{2}{7} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{2}{7} x^{\frac{7}{2}} + C

\frac{u ^{3}}{( u + 1 )}

(cos (x))^{2}

1 - y^{2}

e^{x + 1}

x^{5} (x^{2} + 3)^{4}

What is the integral of sqrt(x)*x^2 ?
The integral of sqrt(x)*x^2 is 2/7 x^{7/2}+C