What is the integral of \sqrt[6]{x^5sqrt(x^4)} ?

The integral of \sqrt[6]{x^5sqrt(x^4)} is 6/13 x^{13/6}+C

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integral of \sqrt[6]{x^5sqrt(x^4)}

\int 6 x^{5} x^{4} d x

\frac{6}{13} x^{\frac{13}{6}} + C

Solution steps

\int 6 x^{5} x^{4} d x

Simplify

6 x^{5} x^{4} : x^{\frac{7}{6}}

= \int x^{\frac{7}{6}} d x

Apply the Power Rule

: \frac{6}{13} x^{\frac{13}{6}}

= \frac{6}{13} x^{\frac{13}{6}}

Add a constant to the solution

= \frac{6}{13} x^{\frac{13}{6}} + C

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What is the integral of \sqrt[6]{x^5sqrt(x^4)} ?
The integral of \sqrt[6]{x^5sqrt(x^4)} is 6/13 x^{13/6}+C