What is the integral from-3 to 3 of-5/(x^3) ?

The integral from-3 to 3 of-5/(x^3) is diverges

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integral from-3 to 3 of-5/(x^3)

\int_{- 3}^{3} - \frac{5}{x ^{3}} d x

diverges

Solution steps

\int_{- 3}^{3} - \frac{5}{x ^{3}} d x

Find undefined (singularity) points:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 3}^{0} - \frac{5}{x ^{3}} d x + \int_{0}^{3} - \frac{5}{x ^{3}} d x

\int_{- 3}^{0} - \frac{5}{x ^{3}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{- 1}^{0} \frac{1}{1 - x} d x

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\int_{- \infty}^{0} x e^{- 3 x} d x

\int_{0}^{2} x e^{4 - x^{2}} d x

\int_{s e c (θ)}^{2} 3 r^{2} sin (θ) d r

What is the integral from-3 to 3 of-5/(x^3) ?
The integral from-3 to 3 of-5/(x^3) is diverges