What is the integral of arcsech(x) ?

The integral of arcsech(x) is xarcsech(x)+2arcsin(1/(sqrt(2))sqrt(x+1))+C

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integral of arcsech(x)

\int arcsech (x) d x

x arcsech (x) + 2 arcsin (\frac{1}{2} x + 1) + C

Solution steps

\int arcsech (x) d x

Apply Integration By Parts

: x arcsech (x) - \int - \frac{1}{x + 1 - x + 1} d x

= x arcsech (x) - \int - \frac{1}{x + 1 - x + 1} d x

\int - \frac{1}{x + 1 - x + 1} d x = - 2 arcsin (\frac{1}{2} x + 1)

= x arcsech (x) - (- 2 arcsin (\frac{1}{2} x + 1))

Simplify

= x arcsech (x) + 2 arcsin (\frac{1}{2} x + 1)

Add a constant to the solution

= x arcsech (x) + 2 arcsin (\frac{1}{2} x + 1) + C

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What is the integral of arcsech(x) ?
The integral of arcsech(x) is xarcsech(x)+2arcsin(1/(sqrt(2))sqrt(x+1))+C