What is the integral of 1/(usqrt(u^2-1)) ?

The integral of 1/(usqrt(u^2-1)) is arctan(sqrt(u^2-1))+C

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integral of 1/(usqrt(u^2-1))

\int \frac{1}{u u ^{2} - 1} d u

arctan (u^{2} - 1) + C

Solution steps

\int \frac{1}{u u ^{2} - 1} d u

Apply u-substitution

= \int \frac{1}{v ^{2} + 1} d v

Use the common integral:

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

= arctan (v)

Substitute back

v = u^{2} - 1

= arctan (u^{2} - 1)

Add a constant to the solution

= arctan (u^{2} - 1) + C

What is the integral of 1/(usqrt(u^2-1)) ?
The integral of 1/(usqrt(u^2-1)) is arctan(sqrt(u^2-1))+C