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

\int \frac{1}{\frac{x}{2} - 3} cos (\frac{x}{2} - 3) d x

(lo g_{2} (x))^{2}

\frac{d}{d x} (\frac{( 3 x ^{7} - 7 x ^{2} + 113 )}{( 5 x ^{3} )})

\frac{\partial}{\partial x} (\frac{x}{y ^{2} + x ^{2}})

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.2 y)

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