# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_{-125}^{\left|∞15\right|}\frac{1}{x^{\frac{1}{3}}}dx$

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Learn how to solve definite integrals problems step by step online.

$\int_{-125}^{\left|\infty15\right|} x^{-\frac{1}{3}}dx$

Learn how to solve definite integrals problems step by step online. Integrate 1/(x^0.3333333333333333) from -125 to abs(\infty15). 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{1}{3}. Evaluate the definite integral. Simplifying.

$\frac{3}{2}\cdot \sqrt[3]{\left|\infty15\right|^{2}}-\frac{75}{2}$
$\int_{-125}^{\left|∞15\right|}\frac{1}{x^{\frac{1}{3}}}dx$