What is the integral from 1 to 4 of 1/(x-3) ?

The integral from 1 to 4 of 1/(x-3) is diverges

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integral from 1 to 4 of 1/(x-3)

\int_{1}^{4} \frac{1}{x - 3} d x

diverges

Solution steps

\int_{1}^{4} \frac{1}{x - 3} d x

Find undefined (singularity) points:

x = 3

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}^{3} \frac{1}{x - 3} d x + \int_{3}^{4} \frac{1}{x - 3} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{0}^{\frac{π}{6}} \frac{1}{cos ^{2} ( 4 x )} d x

What is the integral from 1 to 4 of 1/(x-3) ?
The integral from 1 to 4 of 1/(x-3) is diverges