What is the integral from 1 to 3 of (3x)/(2x^2-6) ?

The integral from 1 to 3 of (3x)/(2x^2-6) is diverges

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integral from 1 to 3 of (3x)/(2x^2-6)

\int_{1}^{3} \frac{3 x}{2 x ^{2} - 6} d x

diverges

Solution steps

\int_{1}^{3} \frac{3 x}{2 x ^{2} - 6} 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{3 x}{2 x ^{2} - 6} d x + \int_{3}^{3} \frac{3 x}{2 x ^{2} - 6} d x

\int_{1}^{3} \frac{3 x}{2 x ^{2} - 6} 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 3 of (3x)/(2x^2-6) ?
The integral from 1 to 3 of (3x)/(2x^2-6) is diverges