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

The integral of (1/(xsqrt(x^2-1))) is arctan(sqrt(x^2-1))+C

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integral of (1/(xsqrt(x^2-1)))

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

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

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2} + 1} d u

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

Use the common integral:

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

= arctan (u)

Substitute back

u = x^{2} - 1

= arctan (x^{2} - 1)

Add a constant to the solution

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

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{- x}

\int - csc (2 w) cot (2 w) d w

\frac{d}{d θ} (cos (θ) - 2 sin (θ))

x \to 0 - lim (a x^{2} + \frac{b}{2})

\frac{2}{x ^{2}}, at (1.2)

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