How do I integrate arctan(x) using integration by parts?

This is an example where we use integration by parts, but it is not immediately obvious where to start.Recall the integration by parts formula ∫u(dv/dx) dx = uv - ∫(du/dx)v dx
KEY STEP:We write arctan(x) = 1 . arctan(x) so that we can set u = arctan(x) and (dv/dx) = 1. Then (du/dx) = 1/(1+x^2) and v = x.
We can now substitute this back into the formula above ∫arctan(x) dx = ∫1 . arctan(x) dx = xarctan(x) - ∫x/(1+x^2) dx
Now the final integral we can recognise to be a natural log integral as d/dx(1+x^2) = 2x. ∫x/(1+x^2) dx = (1/2) ∫2x/(1+x^2) dx = (1/2)ln(1+x^2) + C
Putting all of this together we have finished the integral: ∫arctan(x) dx = xarctan(x) - (1/2)ln(1+x^2) + C.