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:

    “The function of muscle is to pull and not to push, except in the case of the genitals and the tongue.”
    —Leonardo Da Vinci (1425–1519)

    “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)