# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve integrals of rational functions problems step by step online.

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

Learn how to solve integrals of rational functions problems step by step online. Integral of 1/(x^7^(1/5)) with respect to x. Applying the power of a power property. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a constant function, and equals -\frac{7}{5}. As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration.

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

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 0.38 seconds