What is the integral of x^3sqrt(x^3) ?

The integral of x^3sqrt(x^3) is 2/11 x^{11/2}+C

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integral of x^3sqrt(x^3)

\int x^{3} x^{3} d x

\frac{2}{11} x^{\frac{11}{2}} + C

Solution steps

\int x^{3} x^{3} d x

x^{3} = x^{\frac{3}{2}},

assuming

x \geq 0

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

Simplify

x^{3} x^{\frac{3}{2}} : x^{\frac{9}{2}}

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

Apply the Power Rule

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

Add a constant to the solution

= \frac{2}{11} x^{\frac{11}{2}} + C

What is the integral of x^3sqrt(x^3) ?
The integral of x^3sqrt(x^3) is 2/11 x^{11/2}+C