What is the integral of x^2x^{1/2} ?

The integral of x^2x^{1/2} is 2/7 x^{7/2}+C

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integral of x^2x^{1/2}

\int x^{2} x^{\frac{1}{2}} d x

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

Solution steps

\int x^{2} x^{\frac{1}{2}} d x

Simplify

x^{2} x^{\frac{1}{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

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What is the integral of x^2x^{1/2} ?
The integral of x^2x^{1/2} is 2/7 x^{7/2}+C