What is the integral from 3 to 6 of 1/((3x-12)^3) ?

The integral from 3 to 6 of 1/((3x-12)^3) is diverges

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integral from 3 to 6 of 1/((3x-12)^3)

\int_{3}^{6} \frac{1}{( 3 x - 12 ) ^{3}} d x

diverges

Solution steps

\int_{3}^{6} \frac{1}{( 3 x - 12 ) ^{3}} 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}{( 3 x - 12 ) ^{3}} d x + \int_{4}^{6} \frac{1}{( 3 x - 12 ) ^{3}} d x

\int_{3}^{4} \frac{1}{( 3 x - 12 ) ^{3}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{x^{2} + 2}^{3 x} 1 d y

\int_{- 2}^{2} \frac{1}{- 2 ( 1 + x )} d x

\int_{0}^{1} (2 - x - \frac{2}{x + 1}) d x

\int_{0}^{4} x^{3} - x^{2} + 1 d x

\int_{1}^{4} - x^{2} + 8 x d x

What is the integral from 3 to 6 of 1/((3x-12)^3) ?
The integral from 3 to 6 of 1/((3x-12)^3) is diverges