What is the integral from 6 to 7 of x/(x-6) ?

The integral from 6 to 7 of x/(x-6) is diverges

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integral from 6 to 7 of x/(x-6)

\int_{6}^{7} \frac{x}{x - 6} d x

diverges

Solution steps

\int_{6}^{7} \frac{x}{x - 6} d x

Apply u-substitution

: \int_{0}^{1} \frac{u + 6}{u} d u

= \int_{0}^{1} \frac{u + 6}{u} d u

Expand

\frac{u + 6}{u} : 1 + \frac{6}{u}

= \int_{0}^{1} 1 + \frac{6}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} 1 d u + \int_{0}^{1} \frac{6}{u} d u

\int_{0}^{1} 1 d u = 1

\int_{0}^{1} \frac{6}{u} d u =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int (3 x + 2) d x

\int - 1 e^{x} d x

\int \frac{x ^{3}}{3} + 2 x - 5 d x

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

\frac{\partial}{\partial x} (sin (c x))

What is the integral from 6 to 7 of x/(x-6) ?
The integral from 6 to 7 of x/(x-6) is diverges