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

Arccosecant Function Integration Formulas

\int\arccsc(a\,x)\,dx= x\arccsc(a\,x)+ \frac{1}{a}\,\operatorname{artanh}\,\sqrt{1-\frac{1}{a^2\,x^2}}+C
\int x\arccsc(a\,x)\,dx= \frac{x^2\arccsc(a\,x)}{2}+ \frac{x}{2\,a}\sqrt{1-\frac{1}{a^2\,x^2}}+C
\int x^2\arccsc(a\,x)\,dx= \frac{x^3\arccsc(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\arccsc(a\,x)\,dx= \frac{x^{m+1}\arccsc(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)
Lists of integrals
  • Rational functions
  • Irrational functions
  • Trigonometric functions
  • Inverse trigonometric functions
  • Hyperbolic functions
  • Inverse hyperbolic functions
  • Exponential functions
  • Logarithmic functions
  • Gaussian functions

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

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

    “We are thus able to distinguish thinking as the function which is to a large extent linguistic.”
    —Benjamin Lee Whorf (1897–1934)

    “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)