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

The integral of xsqrt(x^3) is 2/7 x^{7/2}+C

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integral of xsqrt(x^3)

\int x x^{3} d x

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

Solution steps

\int x x^{3} d x

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

assuming

x \geq 0

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

Simplify

x x^{\frac{3}{2}} : x^{\frac{5}{2}}

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

Apply the Power Rule

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

Add a constant to the solution

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

What is the integral of xsqrt(x^3) ?
The integral of xsqrt(x^3) is 2/7 x^{7/2}+C