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

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

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = \frac{3}{2}

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{e}^{e^{2}} x ln (x) d x

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