The integral of arctan is x times the inverse tangent of x, minus one-half of the natural logarithm of one plus x squared, plus the constant expressed as C. Using mathematical notation, it is expressed as the integral of arctan(x) dx = x * arctan(x) - (1/2) ln(1+x^2) + C.

The integral of arctan is found by using the integration technique known as integration by parts. Using this technique, u is equal to one plus x squared, and du over dx is 2x. The function arctan is also referred to as the inverse tangent function, notes University of California at Davis.