What is the integral of arctan(sqrt(x^2-1)) ?

The integral of arctan(sqrt(x^2-1)) is xarctan(sqrt(x^2-1))-ln|sqrt(x^2-1)+x|+C

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integral of arctan(sqrt(x^2-1))

\int arctan (x^{2} - 1) d x

x arctan (x^{2} - 1) - ln x^{2} - 1 + x + C

Solution steps

\int arctan (x^{2} - 1) d x

Apply Integration By Parts

: x arctan (x^{2} - 1) - \int \frac{1}{x ^{2} - 1} d x

= x arctan (x^{2} - 1) - \int \frac{1}{x ^{2} - 1} d x

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

= x arctan (x^{2} - 1) - ln x^{2} - 1 + x

Add a constant to the solution

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

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What is the integral of arctan(sqrt(x^2-1)) ?
The integral of arctan(sqrt(x^2-1)) is xarctan(sqrt(x^2-1))-ln|sqrt(x^2-1)+x|+C