List of Integrals of Inverse Trigonometric Functions - Arcsecant Function Integration Formulas

Arcsecant Function Integration Formulas

\int\arcsec(a\,x)\,dx= x\arcsec(a\,x)- \frac{1}{a}\,\operatorname{artanh}\,\sqrt{1-\frac{1}{a^2\,x^2}}+C
\int x\arcsec(a\,x)\,dx= \frac{x^2\arcsec(a\,x)}{2}- \frac{x}{2\,a}\sqrt{1-\frac{1}{a^2\,x^2}}+C
\int x^2\arcsec(a\,x)\,dx= \frac{x^3\arcsec(a\,x)}{3}\,-\, \frac{1}{6\,a^3}\,\operatorname{artanh}\,\sqrt{1-\frac{1}{a^2\,x^2}}\,-\, \frac{x^2}{6\,a}\sqrt{1-\frac{1}{a^2\,x^2}}\,+\,C
\int x^m\arcsec(a\,x)\,dx= \frac{x^{m+1}\arcsec(a\,x)}{m+1}\,-\, \frac{1}{a\,(m+1)}\int \frac{x^{m-1}}{\sqrt{1-\frac{1}{a^2\,x^2}}}\,dx\quad(m\ne-1)


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