What is the integral from 4 to 5 of x/(x-4) ?

The integral from 4 to 5 of x/(x-4) is diverges

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integral from 4 to 5 of x/(x-4)

\int_{4}^{5} \frac{x}{x - 4} d x

diverges

Solution steps

\int_{4}^{5} \frac{x}{x - 4} d x

Apply u-substitution

: \int_{0}^{1} \frac{u + 4}{u} d u

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

Expand

\frac{u + 4}{u} : 1 + \frac{4}{u}

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

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\frac{\partial}{\partial x} ((y^{2} - 2)^{3})

\frac{1}{3 s + 5}

\frac{d}{d x} (\frac{x ^{2} + 3 x}{- 6})

\frac{d y}{d x} - 4 y = \frac{48 x}{y ^{2}}

\frac{\partial}{\partial x} (ln (x^{6} + y^{7}))

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