What is the integral from 2 to 4 of (x^2+1)/(x^2-5) ?

The integral from 2 to 4 of (x^2+1)/(x^2-5) is diverges

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integral from 2 to 4 of (x^2+1)/(x^2-5)

\int_{2}^{4} \frac{x ^{2} + 1}{x ^{2} - 5} d x

diverges

Solution steps

\int_{2}^{4} \frac{x ^{2} + 1}{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_{2}^{5} \frac{x ^{2} + 1}{x ^{2} - 5} d x + \int_{5}^{4} \frac{x ^{2} + 1}{x ^{2} - 5} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int x^{3} cos (x^{2}) d x

\int x x - 9 d x

3 x y^{3} + 4 x y = 28, (4, 1)

x \to 2 lim (3 x^{2} - x - 10)

\frac{d ^{2} y}{d x ^{2}} - 2 x \frac{d y}{d x} + 2 y = 0

What is the integral from 2 to 4 of (x^2+1)/(x^2-5) ?
The integral from 2 to 4 of (x^2+1)/(x^2-5) is diverges