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

Arccotangent Function Integration Formulas

\int\arccot(a\,x)\,dx= x\arccot(a\,x)+ \frac{\ln\left(a^2\,x^2+1\right)}{2\,a}+C
\int x\arccot(a\,x)\,dx= \frac{x^2\arccot(a\,x)}{2}+ \frac{\arccot(a\,x)}{2\,a^2}+\frac{x}{2\,a}+C
\int x^2\arccot(a\,x)\,dx= \frac{x^3\arccot(a\,x)}{3}- \frac{\ln\left(a^2\,x^2+1\right)}{6\,a^3}+\frac{x^2}{6\,a}+C
\int x^m\arccot(a\,x)\,dx= \frac{x^{m+1}\arccot(a\,x)}{m+1}+ \frac{a}{m+1}\int \frac{x^{m+1}}{a^2\,x^2+1}\,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:

    “To look backward for a while is to refresh the eye, to restore it, and to render it the more fit for its prime function of looking forward.”
    —Margaret Fairless Barber (1869–1901)

    “The more specific idea of evolution now reached is—a change from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity, accompanying the dissipation of motion and integration of matter.”
    —Herbert Spencer (1820–1903)

    “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)