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Simplify $\sqrt[5]{x^7}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $7$ and $n$ equals $\frac{1}{5}$
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$\int\frac{1}{\sqrt[5]{x^{7}}}dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(x^7^1/5))dx. Simplify \sqrt[5]{x^7} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 7 and n equals \frac{1}{5}. 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 number or constant function, such as -\frac{7}{5}. Divide 1 by -\frac{2}{5}.