What is the integral from-2 to 2 of 1/x ?

The integral from-2 to 2 of 1/x is diverges

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integral from-2 to 2 of 1/x

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

diverges

Solution steps

\int_{- 2}^{2} \frac{1}{x} 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{1}{x} d x + \int_{0}^{2} \frac{1}{x} d x

\int_{- 2}^{0} \frac{1}{x} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

x \to - 2 lim (\frac{x}{x + 2})

x \to \infty lim (e^{- 8 x^{2}})

y = (x - 2)^{2}, y = 2 x - 1

\frac{\partial}{\partial x} (5 x^{2} y^{3})

What is the integral from-2 to 2 of 1/x ?
The integral from-2 to 2 of 1/x is diverges