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

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

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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