What is the integral from 3 to infinity of 5/(x^2-x) ?

The integral from 3 to infinity of 5/(x^2-x) is -5(ln(2)-ln(3))

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integral from 3 to infinity of 5/(x^2-x)

\int_{3}^{\infty} \frac{5}{x ^{2} - x} d x

- 5 (ln (2) - ln (3))

Decimal Notation

2.02732 \dots

Solution steps

\int_{3}^{\infty} \frac{5}{x ^{2} - x} d x

Compute the indefinite integral:

\int \frac{5}{x ^{2} - x} d x = 5 (- ln ∣ x ∣ + ln ∣ x - 1 ∣) + C

Compute the boundaries:

\int_{3}^{\infty} \frac{5}{x ^{2} - x} d x = 0 - 5 (- ln (3) + ln (2))

= 0 - 5 (- ln (3) + ln (2))

Simplify

= - 5 (ln (2) - ln (3))

\frac{d}{d x} (2 π \frac{l}{g ( x )})

\int (1 + cot^{2} (θ)) (csc^{2} (θ)) d θ

y^{^{''}} + 2 y^{^{'}} + y = 1

y^{^{''}} - y^{^{'}} + 9 y = 3 sin (3 t)

x \to + 2 lim (\frac{1}{2})

What is the integral from 3 to infinity of 5/(x^2-x) ?
The integral from 3 to infinity of 5/(x^2-x) is -5(ln(2)-ln(3))