What is the integral of xarcsec(x) ?

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

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integral of xarcsec(x)

\int x arcsec (x) d x

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

Solution steps

\int x arcsec (x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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

f (x) = \frac{1}{x}, at x = - 2

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x)

\frac{d}{d x} (2 e^{x^{2}})

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

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