What is the integral from 3 to infinity of 4/(x^2-x) ?

The integral from 3 to infinity of 4/(x^2-x) is -4(ln(2)-ln(3))

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integral from 3 to infinity of 4/(x^2-x)

\int_{3}^{\infty} \frac{4}{x ^{2} - x} d x

- 4 (ln (2) - ln (3))

Decimal Notation

1.62186 \dots

Solution steps

\int_{3}^{\infty} \frac{4}{x ^{2} - x} d x

Compute the indefinite integral:

\int \frac{4}{x ^{2} - x} d x = 4 (- ln ∣ x ∣ + ln ∣ x - 1 ∣) + C

Compute the boundaries:

\int_{3}^{\infty} \frac{4}{x ^{2} - x} d x = 0 - 4 (- ln (3) + ln (2))

= 0 - 4 (- ln (3) + ln (2))

Simplify

= - 4 (ln (2) - ln (3))

\int 8 x ln (2 x) d x

x \to 1 lim (x^{2} + x - 3)

y^{^{'}} = 2 sin (x) + 1 + y

f (x) = x^{3} + 2 x, at x = - 3

n = 1 \sum \infty (\frac{1}{n})^{n}

What is the integral from 3 to infinity of 4/(x^2-x) ?
The integral from 3 to infinity of 4/(x^2-x) is -4(ln(2)-ln(3))