What is the integral from 1 to 12 of 1/(x-7) ?

The integral from 1 to 12 of 1/(x-7) is diverges

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integral from 1 to 12 of 1/(x-7)

\int_{1}^{12} \frac{1}{x - 7} d x

diverges

Solution steps

\int_{1}^{12} \frac{1}{x - 7} d x

Find undefined (singularity) points:

x = 7

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}^{7} \frac{1}{x - 7} d x + \int_{7}^{12} \frac{1}{x - 7} d x

\int_{1}^{7} \frac{1}{x - 7} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2})

\int x^{2} + 2 x + 1 d x

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

\int_{0}^{1} \frac{2 y}{e ^{2 y}} d y

\frac{d}{d x} (- (x - 5)^{2})

What is the integral from 1 to 12 of 1/(x-7) ?
The integral from 1 to 12 of 1/(x-7) is diverges