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

The integral of 1/(|x|sqrt(x^2-1)) is arcsec(x)+C

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integral of 1/(|x|sqrt(x^2-1))

\int \frac{1}{∣ x ∣ x ^{2} - 1} d x

arcsec (x) + C

Solution steps

\int \frac{1}{∣ x ∣ x ^{2} - 1} d x

Use the common integral:

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

= arcsec (x)

Add a constant to the solution

= arcsec (x) + C

\int \frac{x}{x ^{2} + 1} - \frac{3}{3 x + 1} d x

f (y) = 3 y^{2}

\frac{d}{d x} (2 x^{3} - 3 x^{2} - 72 x + 15)

\frac{d}{d x} (\frac{1}{4} ln (cos (4 x)))

\int \frac{1}{1 + e ^{x}} d x

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