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

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

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

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

2 ln (2)

Decimal Notation

1.38629 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 2 ln (2))

Simplify

= 2 ln (2)

\frac{d}{d x} (ln (x ln (x)))

\frac{d y}{d x} = 5^{x} ln (5) + \frac{2}{x ^{2} + 1}

X^{5}

y^{^{''}} + 9 y = x e^{x}

\int_{1200}^{1201} 0.1

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