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

Arctangent Function Integration Formulas

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

    “Every boy was supposed to come into the world equipped with a father whose prime function was to be our father and show us how to be men. He can escape us, but we can never escape him. Present or absent, dead or alive, real or imagined, our father is the main man in our masculinity.”
    —Frank Pittman (20th century)

    “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)

    “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)