What is the integral of x^3sqrt(x^7) ?

The integral of x^3sqrt(x^7) is 2/15 x^{15/2}+C

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integral of x^3sqrt(x^7)

\int x^{3} x^{7} d x

\frac{2}{15} x^{\frac{15}{2}} + C

Solution steps

\int x^{3} x^{7} d x

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

assuming

x \geq 0

= \int x^{3} x^{\frac{7}{2}} d x

Simplify

x^{3} x^{\frac{7}{2}} : x^{\frac{13}{2}}

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

Apply the Power Rule

: \frac{2}{15} x^{\frac{15}{2}}

= \frac{2}{15} x^{\frac{15}{2}}

Add a constant to the solution

= \frac{2}{15} x^{\frac{15}{2}} + C

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What is the integral of x^3sqrt(x^7) ?
The integral of x^3sqrt(x^7) is 2/15 x^{15/2}+C