What is the integral of \sqrt[7]{x^6} ?

The integral of \sqrt[7]{x^6} is 7/13 x^{13/7}+C

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integral of \sqrt[7]{x^6}

\frac{7}{13} x^{\frac{13}{7}} + C

Solution steps

assuming

x \geq 0

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

Apply the Power Rule

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

= \frac{7}{13} x^{\frac{13}{7}}

Add a constant to the solution

= \frac{7}{13} x^{\frac{13}{7}} + C

\frac{\partial}{\partial y} (3 x - 2 y^{4})

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

x = - 2, x = 3, y = x^{2} - 12, y = x - 6

1 - x^{12}

\frac{\partial ^{2}}{\partial x ^{2}} (\frac{1}{x y})

What is the integral of \sqrt[7]{x^6} ?
The integral of \sqrt[7]{x^6} is 7/13 x^{13/7}+C