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Step-by-step Solution

Integrate $\frac{1}{x^{\frac{1}{3}}}$ from $-\infty $ to $-1$

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Step-by-step explanation

Problem to solve:

$\int_{-\infty}^{-1}\frac{1}{\sqrt[3]{x}}dx$

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

$\lim_{c\to{-\infty }}\:\int_{c}^{-1}\frac{1}{\sqrt[3]{x}}dx$

Unlock this full step-by-step solution!

Learn how to solve definite integrals problems step by step online. Integrate 1/(x^(1/3)) from -\infty to -1. Replace the integral's limit by a finite value. 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{1}{3}. Evaluate the definite integral.

Answer

$-\frac{3}{2}\left(1+\sqrt[3]{\left(-\infty \right)^{2}}\right)$

Problem Analysis