Calculus  Integrals
posted by Sean .
What is the integral of arctan x?

Sorry. I lied.
Misread the question.
What is the indefinite integral of arccot(4x) ? 
arccot is simply related to arctan:
arccot(x) = pi/2  arctan(x)
You can integrate arctan using partial integration. You get x arctan(x)  integral of xdx/(x^2+1), the latter integrand contans in the denominater the derivative of the numerator (up to a factor 2), so you get a logarithmic function.