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

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

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integral from-2 to 2 of 1/(-2(1+x))

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = - 1

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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

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\int_{1}^{4} - x^{2} + 8 x d x

\int_{0}^{π} 2 e^{x} sin (x) d x

\int_{e^{3}}^{e^{5}} \frac{1}{x ln ( x )} d x

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