# Step-by-step Solution

## Integral of $\frac{1}{\left(x^7\right)^{\left(\frac{1}{5}\right)}}$ with respect to x

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### Videos

$-\frac{5}{2}x^{-\frac{2}{5}}+C_0$

## Step-by-step explanation

Problem to solve:

$\int\frac{1}{\sqrt[5]{x^7}}dx$
1

Applying the power of a power property

$\int\frac{1}{\sqrt[5]{x^{7}}}dx$
2

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int x^{-\frac{7}{5}}dx$

$-\frac{5}{2}x^{-\frac{2}{5}}+C_0$
$\int\frac{1}{\sqrt[5]{x^7}}dx$

### Main topic:

Integrals of Rational Functions

~ 0.83 seconds

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