What is the integral from 4 to 6 of 1/(x^2-25) ?

The integral from 4 to 6 of 1/(x^2-25) is diverges

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integral from 4 to 6 of 1/(x^2-25)

\int_{4}^{6} \frac{1}{x ^{2} - 25} d x

diverges

Solution steps

\int_{4}^{6} \frac{1}{x ^{2} - 25} 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_{4}^{5} \frac{1}{x ^{2} - 25} d x + \int_{5}^{6} \frac{1}{x ^{2} - 25} d x

\int_{4}^{5} \frac{1}{x ^{2} - 25} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{0}^{\frac{π}{14}} sin^{5} (7 x) d x

\int_{11}^{\infty} \frac{1}{x ^{6}} d x

\int_{π - α}^{2 π} - 1

\int_{0.5}^{1} \frac{3}{4} x (1 - 0.25 x) d x

\int_{- 1}^{7} (∣ x - 2 ∣ - 3) d x

What is the integral from 4 to 6 of 1/(x^2-25) ?
The integral from 4 to 6 of 1/(x^2-25) is diverges