What is the integral from-8 to 2 of 1/(x+6) ?

The integral from-8 to 2 of 1/(x+6) is diverges

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integral from-8 to 2 of 1/(x+6)

\int_{- 8}^{2} \frac{1}{x + 6} d x

diverges

Solution steps

\int_{- 8}^{2} \frac{1}{x + 6} d x

Find undefined (singularity) points:

x = - 6

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_{- 8}^{- 6} \frac{1}{x + 6} d x + \int_{- 6}^{2} \frac{1}{x + 6} d x

\int_{- 8}^{- 6} \frac{1}{x + 6} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{- 3}^{8} (- 14 + 6 x) d x

\int_{- 1}^{1} y \cdot 1 - y^{2} d y

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} y d y

\int_{0}^{1} \frac{5}{2} y^{\frac{3}{2}} d y

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} x d x

What is the integral from-8 to 2 of 1/(x+6) ?
The integral from-8 to 2 of 1/(x+6) is diverges