What is the integral from 3 to 7 of x/(x-7) ?

The integral from 3 to 7 of x/(x-7) is diverges

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integral from 3 to 7 of x/(x-7)

\int_{3}^{7} \frac{x}{x - 7} d x

diverges

Solution steps

\int_{3}^{7} \frac{x}{x - 7} d x

Apply u-substitution

: \int_{- 4}^{0} \frac{u + 7}{u} d u

= \int_{- 4}^{0} \frac{u + 7}{u} d u

Expand

\frac{u + 7}{u} : 1 + \frac{7}{u}

= \int_{- 4}^{0} 1 + \frac{7}{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_{- 4}^{0} 1 d u + \int_{- 4}^{0} \frac{7}{u} d u

\int_{- 4}^{0} 1 d u = 4

\int_{- 4}^{0} \frac{7}{u} d u =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{7}^{12} \frac{900}{x + 13} - 35 d x

What is the integral from 3 to 7 of x/(x-7) ?
The integral from 3 to 7 of x/(x-7) is diverges