What is the integral from 0 to 1 of 1/((3x-2)^4) ?

The integral from 0 to 1 of 1/((3x-2)^4) is diverges

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integral from 0 to 1 of 1/((3x-2)^4)

\int_{0}^{1} \frac{1}{( 3 x - 2 ) ^{4}} d x

diverges

Solution steps

\int_{0}^{1} \frac{1}{( 3 x - 2 ) ^{4}} d x

Find undefined (singularity) points:

x = \frac{2}{3}

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_{0}^{\frac{2}{3}} \frac{1}{( 3 x - 2 ) ^{4}} d x + \int_{\frac{2}{3}}^{1} \frac{1}{( 3 x - 2 ) ^{4}} d x

\int_{0}^{\frac{2}{3}} \frac{1}{( 3 x - 2 ) ^{4}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

What is the integral from 0 to 1 of 1/((3x-2)^4) ?
The integral from 0 to 1 of 1/((3x-2)^4) is diverges