What is the integral from 1 to 5 of 1/(x-2) ?

The integral from 1 to 5 of 1/(x-2) is diverges

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integral from 1 to 5 of 1/(x-2)

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = 2

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_{1}^{2} \frac{1}{x - 2} d x + \int_{2}^{5} \frac{1}{x - 2} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

n = 1 \sum \infty \frac{n}{1 + 3 n}

n = 1 \sum \infty \frac{1}{n ^{0.5}}

\frac{d}{d t} (4 e^{- 3 t})

\frac{d}{d A} (- cos (2) (A) - sin (2) (A))

\int \frac{1}{x + y} d x

What is the integral from 1 to 5 of 1/(x-2) ?
The integral from 1 to 5 of 1/(x-2) is diverges