What is the integral from-e to e of 1/(|x|) ?

The integral from-e to e of 1/(|x|) is diverges

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integral from-e to e of 1/(|x|)

\int_{- e}^{e} \frac{1}{∣ x ∣} d x

diverges

Solution steps

\int_{- e}^{e} \frac{1}{∣ x ∣} d x

Eliminate Absolutes

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

1 + 2 x

\int \frac{x ^{2} + 1}{x ( x ^{2} - 1 )} d x

f (x) = \frac{5 + csc ( x )}{9 - csc ( x )}

g

\int \frac{1}{9 - 49 x ^{2}} d x

What is the integral from-e to e of 1/(|x|) ?
The integral from-e to e of 1/(|x|) is diverges