What is the integral from 0 to 5 of w/(w^2-2) ?

The integral from 0 to 5 of w/(w^2-2) is diverges

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integral from 0 to 5 of w/(w^2-2)

\int_{0}^{5} \frac{w}{w ^{2} - 2} d w

diverges

Solution steps

\int_{0}^{5} \frac{w}{w ^{2} - 2} d w

Find undefined (singularity) points:

w = 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_{0}^{2} \frac{w}{w ^{2} - 2} d w + \int_{2}^{5} \frac{w}{w ^{2} - 2} d w

\int_{0}^{2} \frac{w}{w ^{2} - 2} d w =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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

\int_{0}^{2 - x} \frac{3}{4} y d y

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

\int_{0}^{6} 3 x^{2} - 24 x + 45 d x

\int_{0}^{\frac{5 π}{4}} sec^{4} (\frac{t}{5}) d t

What is the integral from 0 to 5 of w/(w^2-2) ?
The integral from 0 to 5 of w/(w^2-2) is diverges