What is the integral from 1 to 3 of 1/(x^2-2x) ?

The integral from 1 to 3 of 1/(x^2-2x) is diverges

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integral from 1 to 3 of 1/(x^2-2x)

\int_{1}^{3} \frac{1}{x ^{2} - 2 x} d x

diverges

Solution steps

\int_{1}^{3} \frac{1}{x ^{2} - 2 x} 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} - 2 x} d x + \int_{2}^{3} \frac{1}{x ^{2} - 2 x} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{- 2}^{0} x d x

\int_{0}^{\frac{π}{2}} cos (x) - sin (x) d x

\int_{1}^{2} \frac{1}{x ^{2}} e^{\frac{1}{x}} d x

What is the integral from 1 to 3 of 1/(x^2-2x) ?
The integral from 1 to 3 of 1/(x^2-2x) is diverges