Step-by-step Solution

Integrate $\frac{1}{\sqrt[3]{x}}$ from $-125$ to $\left|\infty15\right|$

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Step-by-step explanation

Problem to solve:

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

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

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

Unlock this full step-by-step solution!

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 constant function, and equals -\frac{1}{3}. Evaluate the definite integral. Simplifying.

Final Answer

$1.5\cdot \sqrt[3]{\left|\infty15\right|^{2}}+37.5$

Problem Analysis

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

Main topic:

Definite integrals

Time to solve it:

~ 0.07 seconds