What is the integral from 2 to infinity of 2/(x^2-1) ?

The integral from 2 to infinity of 2/(x^2-1) is ln(3)

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integral from 2 to infinity of 2/(x^2-1)

\int_{2}^{\infty} \frac{2}{x ^{2} - 1} d x

ln (3)

Decimal Notation

1.09861 \dots

Solution steps

\int_{2}^{\infty} \frac{2}{x ^{2} - 1} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{2}^{\infty} \frac{2}{x ^{2} - 1} d x = 0 - (- ln (3))

= 0 - (- ln (3))

Simplify

= ln (3)

x \to + 0 lim (ln (x^{2}))

\frac{2 s + 1}{2 s ^{2} + s + 1}

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\int \frac{2 sin ^{3} ( x )}{x} d x

\int \frac{44 - x}{x ^{2} + 2 x - 24} d x

What is the integral from 2 to infinity of 2/(x^2-1) ?
The integral from 2 to infinity of 2/(x^2-1) is ln(3)