What is the integral from 3 to 5 of 5/((x-4)^2) ?

The integral from 3 to 5 of 5/((x-4)^2) is diverges

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integral from 3 to 5 of 5/((x-4)^2)

\int_{3}^{5} \frac{5}{( x - 4 ) ^{2}} d x

diverges

Solution steps

\int_{3}^{5} \frac{5}{( x - 4 ) ^{2}} 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{5}{( x - 4 ) ^{2}} d x + \int_{4}^{5} \frac{5}{( x - 4 ) ^{2}} d x

\int_{3}^{4} \frac{5}{( x - 4 ) ^{2}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{3} x e^{3 x} d x

\int_{- 8}^{2} \frac{1}{x + 6} d x

\int_{- 3}^{8} (- 14 + 6 x) d x

\int_{- 1}^{1} y \cdot 1 - y^{2} d y

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} y d y

What is the integral from 3 to 5 of 5/((x-4)^2) ?
The integral from 3 to 5 of 5/((x-4)^2) is diverges