What is the integral from 1 to e of x/(x^2-5) ?

The integral from 1 to e of x/(x^2-5) is diverges

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integral from 1 to e of x/(x^2-5)

\int_{1}^{e} \frac{x}{x ^{2} - 5} d x

diverges

Solution steps

\int_{1}^{e} \frac{x}{x ^{2} - 5} d x

Find undefined (singularity) points:

x = 5

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}^{5} \frac{x}{x ^{2} - 5} d x + \int_{5}^{e} \frac{x}{x ^{2} - 5} d x

\int_{1}^{5} \frac{x}{x ^{2} - 5} 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 e of x/(x^2-5) ?
The integral from 1 to e of x/(x^2-5) is diverges