What is the integral from 1 to 10 of 1/(x-6) ?

The integral from 1 to 10 of 1/(x-6) is diverges

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integral from 1 to 10 of 1/(x-6)

\int_{1}^{10} \frac{1}{x - 6} d x

diverges

Solution steps

\int_{1}^{10} \frac{1}{x - 6} d x

Find undefined (singularity) points:

x = 6

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}^{6} \frac{1}{x - 6} d x + \int_{6}^{10} \frac{1}{x - 6} d x

\int_{1}^{6} \frac{1}{x - 6} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

f (x) = 5 x^{2}, at x = - 3, - 45

f (x) = x^{3} - 4 x

\frac{d}{d x} (\frac{sin ( x ^{2} )}{3 x})

\int x e^{x} d x

2 x y^{^{'}} + y = 6 x, y (4) = 26

What is the integral from 1 to 10 of 1/(x-6) ?
The integral from 1 to 10 of 1/(x-6) is diverges