You can find the derivative of arctan using the chain rule.
If you don't know the antiderivative of arctan x off the top of your head, that's to be expected. Thankfully there's a hidden factor of 1, so we can use integration by parts.Since we don't know the antiderivative of arctan x we can't use that for v', so we need to pick
u = arctan x
v' = 1
The derivative of arctan x is
which you could figure out using the chain rule, so
u' = (1 + x2)-1
v = x.
Put everything in the formula:
Integrating the new integral by substitution (taking u = (1 + x2) so u' = 2x) we get