What is the integral from-2 to 5 of-5/(x^2) ?

The integral from-2 to 5 of-5/(x^2) is diverges

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integral from-2 to 5 of-5/(x^2)

\int_{- 2}^{5} - \frac{5}{x ^{2}} d x

diverges

Solution steps

\int_{- 2}^{5} - \frac{5}{x ^{2}} 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_{- 2}^{0} - \frac{5}{x ^{2}} d x + \int_{0}^{5} - \frac{5}{x ^{2}} d x

\int_{- 2}^{0} - \frac{5}{x ^{2}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{2} \frac{x ^{2} + 2}{x ^{2}} d x

\int_{0}^{5} e^{- s t} (2 t) d t

\int_{0}^{5} t^{2} + 2 t - 3 d t

\int_{2}^{\infty} \frac{2}{4 + x ^{2}} d x

\int_{0}^{2 x} arctan (t) d t

What is the integral from-2 to 5 of-5/(x^2) ?
The integral from-2 to 5 of-5/(x^2) is diverges