What is the integral of x*sqrt(x^9) ?

The integral of x*sqrt(x^9) is 2/13 x^{13/2}+C

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integral of x*sqrt(x^9)

\int x \cdot x^{9} d x

\frac{2}{13} x^{\frac{13}{2}} + C

Solution steps

\int x x^{9} d x

x^{9} = x^{\frac{9}{2}},

assuming

x \geq 0

= \int x x^{\frac{9}{2}} d x

Simplify

x x^{\frac{9}{2}} : x^{\frac{11}{2}}

= \int x^{\frac{11}{2}} d x

Apply the Power Rule

= \frac{2}{13} x^{\frac{13}{2}}

Add a constant to the solution

= \frac{2}{13} x^{\frac{13}{2}} + C

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What is the integral of x*sqrt(x^9) ?
The integral of x*sqrt(x^9) is 2/13 x^{13/2}+C