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

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

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

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

diverges

Solution steps

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{2}^{3} (2 + 2 y)^{2} d y

\int_{0}^{1} - 1 + \frac{π x}{2} d x

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

\int_{3}^{4} - x ln (x - 3) d x

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

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