What is the integral of arcsec(x) ?

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

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integral of arcsec(x)

\int arcsec (x) d x

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

Solution steps

\int arcsec (x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x}{a x ^{2} + b})

x \to - 4 - lim (x^{2} + \frac{5}{x + 4})

\int \frac{1}{1 - 0.5 x} d x

x \to 10 - lim (8 - x)

\frac{\partial}{\partial z} (x e^{z} + x y + z^{3} - 4)

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