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)


Read more about this topic:  List Of Integrals Of Inverse Trigonometric Functions

Famous quotes containing the words function, integration and/or formulas:

    “If the children and youth of a nation are afforded opportunity to develop their capacities to the fullest, if they are given the knowledge to understand the world and the wisdom to change it, then the prospects for the future are bright. In contrast, a society which neglects its children, however well it may function in other respects, risks eventual disorganization and demise.”
    —Urie Bronfenbrenner (b. 1917)

    “The only phenomenon with which writing has always been concomitant is the creation of cities and empires, that is the integration of large numbers of individuals into a political system, and their grading into castes or classes.... It seems to have favored the exploitation of human beings rather than their enlightenment.”
    —Claude Lévi-Strauss (b. 1908)

    “You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”
    —Hermann Hesse (1877–1962)