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:

    “Any translation which intends to perform a transmitting function cannot transmit anything but information—hence, something inessential. This is the hallmark of bad translations.”
    —Walter Benjamin (1892–1940)

    “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)

    “That’s the great danger of sectarian opinions, they always accept the formulas of past events as useful for the measurement of future events and they never are, if you have high standards of accuracy.”
    —John Dos Passos (1896–1970)