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:

    “The information links are like nerves that pervade and help to animate the human organism. The sensors and monitors are analogous to the human senses that put us in touch with the world. Data bases correspond to memory; the information processors perform the function of human reasoning and comprehension. Once the postmodern infrastructure is reasonably integrated, it will greatly exceed human intelligence in reach, acuity, capacity, and precision.”
    —Albert Borgman, U.S. educator, author. Crossing the Postmodern Divide, ch. 4, University of Chicago Press (1992)

    “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)

    “It is sentimentalism to assume that the teaching of life can always be fitted to the child’s interests, just as it is empty formalism to force the child to parrot the formulas of adult society. Interests can be created and stimulated.”
    —Jerome S. Bruner (20th century)