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Step-by-step Solution

Integrate 1/(x^3) from -\infty to -1

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Answer

$-\frac{1}{2}$

Step-by-step explanation

Problem to solve:

$\int_{-\infty}^{-1}\left(\frac{1}{x^3}\right)dx$
1

Replace the integral's limit by a finite value

$\lim_{c\to{-1\infty}}\:\int_{c}^{-1}\frac{1}{x^3}dx$
2

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

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

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Answer

$-\frac{1}{2}$

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$\int_{-\infty}^{-1}\left(\frac{1}{x^3}\right)dx$

Main topic:

Integral calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.6 seconds