What is the integral from 3 to 5 of 1/(x-4) ?

The integral from 3 to 5 of 1/(x-4) is diverges

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integral from 3 to 5 of 1/(x-4)

\int_{3}^{5} \frac{1}{x - 4} d x

diverges

Solution steps

\int_{3}^{5} \frac{1}{x - 4} d x

Find undefined (singularity) points:

x = 4

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}^{4} \frac{1}{x - 4} d x + \int_{4}^{5} \frac{1}{x - 4} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

y = (x^{2} - 4 x)^{5}

\int_{1}^{\infty} e^{- x} d x

(x^{x^{x^{x}}})^{^{'}}

(7 x + 6 y) d x + (6 x - 8 y 3) d y = 0

x \to 0 lim (\frac{sin ( 7 x )}{x})

What is the integral from 3 to 5 of 1/(x-4) ?
The integral from 3 to 5 of 1/(x-4) is diverges