What is the integral of 1/(\sqrt[7]{3-5x)} ?

The integral of 1/(\sqrt[7]{3-5x)} is -7/30 (3-5x)^{6/7}+C

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integral of 1/(\sqrt[7]{3-5x)}

- \frac{7}{30} (3 - 5 x)^{\frac{6}{7}} + C

Solution steps

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply the Power Rule

: \frac{7}{6} u^{\frac{6}{7}}

= - \frac{1}{5} \cdot \frac{7}{6} u^{\frac{6}{7}}

Substitute back

u = 3 - 5 x

= - \frac{1}{5} \cdot \frac{7}{6} (3 - 5 x)^{\frac{6}{7}}

Simplify

- \frac{1}{5} \cdot \frac{7}{6} (3 - 5 x)^{\frac{6}{7}} : - \frac{7}{30} (3 - 5 x)^{\frac{6}{7}}

= - \frac{7}{30} (3 - 5 x)^{\frac{6}{7}}

Add a constant to the solution

= - \frac{7}{30} (3 - 5 x)^{\frac{6}{7}} + C

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What is the integral of 1/(\sqrt[7]{3-5x)} ?
The integral of 1/(\sqrt[7]{3-5x)} is -7/30 (3-5x)^{6/7}+C