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

The integral from 2 to 3 of 1/(xsqrt(x^2-1)) is arctan(2sqrt(2))-pi/3

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

\int_{2}^{3} \frac{1}{x x ^{2} - 1} d x

arctan (22) - \frac{π}{3}

Decimal Notation

0.18376 \dots

Solution steps

\int_{2}^{3} \frac{1}{x x ^{2} - 1} d x

Apply u-substitution

: \int_{3}^{22} \frac{1}{u ^{2} + 1} d u

= \int_{3}^{22} \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= [arctan (u)]_{3}^{22}

Compute the boundaries:

arctan (22) - \frac{π}{3}

= arctan (22) - \frac{π}{3}

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What is the integral from 2 to 3 of 1/(xsqrt(x^2-1)) ?
The integral from 2 to 3 of 1/(xsqrt(x^2-1)) is arctan(2sqrt(2))-pi/3