What is the integral from-5 to 5 of 1/x ?

The integral from-5 to 5 of 1/x is diverges

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integral from-5 to 5 of 1/x

\int_{- 5}^{5} \frac{1}{x} d x

diverges

Solution steps

\int_{- 5}^{5} \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_{- 5}^{0} \frac{1}{x} d x + \int_{0}^{5} \frac{1}{x} d x

\int_{- 5}^{0} \frac{1}{x} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

y^{^{''}} + 10 y^{^{'}} + 25 y = t^{- 2} e^{- 5 t}

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

\frac{d}{d x} (x (4 x - 5)^{3})

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

x \to 1 lim (\frac{4 x + 3}{2 x + 1})

What is the integral from-5 to 5 of 1/x ?
The integral from-5 to 5 of 1/x is diverges