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

The integral from 2 to 3 of ln(x^2-1) is 10ln(2)-2-3ln(3)

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integral from 2 to 3 of ln(x^2-1)

\int_{2}^{3} ln (x^{2} - 1) d x

10 ln (2) - 2 - 3 ln (3)

Decimal

1.63563 \dots

Solution steps

\int_{2}^{3} ln (x^{2} - 1) d x

Apply Integration By Parts

: [x ln (x^{2} - 1) - \int \frac{2 x ^{2}}{x ^{2} - 1} d x]_{2}^{3}

= [x ln (x^{2} - 1) - \int \frac{2 x ^{2}}{x ^{2} - 1} d x]_{2}^{3}

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

= [x ln (x^{2} - 1) - (- ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + 2 x)]_{2}^{3}

Simplify

= [x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x]_{2}^{3}

Compute the boundaries:

10 ln (2) - 2 - 3 ln (3)

= 10 ln (2) - 2 - 3 ln (3)

\int_{- 2}^{x} (t^{2} - 2 t) d t

\int_{3}^{7} \frac{10}{x ^{2}} d x

\int_{0}^{2} \frac{2 x}{3 - x} d x

\int_{1}^{25} \frac{11}{x} d x

\int_{1}^{3} e^{x} - e d x

What is the integral from 2 to 3 of ln(x^2-1) ?
The integral from 2 to 3 of ln(x^2-1) is 10ln(2)-2-3ln(3)