Inverse tangent integral

The inverse tangent integral typically refers to the integral defined by the function: \[ \int \frac{1}{1+x^2} \, dx = \tan^{-1}(x) + C \] where \( \tan^{-1}(x) \), also known as the arctangent function, is the inverse of the tangent function. The integral evaluates to the arctangent of \( x \), plus a constant of integration \( C \).