What is the integral from 0 to 2 of 1/(x^2-7x+6) ?

The integral from 0 to 2 of 1/(x^2-7x+6) is diverges

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integral from 0 to 2 of 1/(x^2-7x+6)

\int_{0}^{2} \frac{1}{x ^{2} - 7 x + 6} d x

diverges

Solution steps

\int_{0}^{2} \frac{1}{x ^{2} - 7 x + 6} d x

Find undefined (singularity) points:

x = 1

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}^{1} \frac{1}{x ^{2} - 7 x + 6} d x + \int_{1}^{2} \frac{1}{x ^{2} - 7 x + 6} d x

\int_{0}^{1} \frac{1}{x ^{2} - 7 x + 6} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int \frac{36 x ^{2} - 49}{x ^{3}} d x

x \to \frac{π}{2} - lim (sec (x))

\frac{d y}{d x} = e^{8 x - 3 y}, y (0) = 4

f (x) = \frac{x ^{2}}{( 4 + x )}

- 9 x^{\frac{1}{3}} + 5, at x = 27

What is the integral from 0 to 2 of 1/(x^2-7x+6) ?
The integral from 0 to 2 of 1/(x^2-7x+6) is diverges