Step-by-step Solution

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

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$-0.5$

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

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

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

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

$-0.5$
$\int_{-\infty}^{-1}\left(\frac{1}{x^3}\right)dx$