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)

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