Find the antiderivative of f(x)=1/(1+x^2)*arctanx.

To find the anti derivative of f(x)=1/(1+x^2)*arctan
x.

Int f(x) dx = Int {dx/(1+x^2)}*arctan
x.

Put arctan x = t,    dx/(1+x^2 =
dt.

Therefore Int f(x) dx = (1/1+x^2)t * dx =
tdt.

Int f(x) = t^2/2 = (1/2)(arctan x)
+C.

Also if you meant  f(x) =
1/{(1+x^2)*arctanx},

Then Int f(x) dx =Int{ 1/[(1+x^2)
arctan x]} dx = dt/t.

Int f(x) dx = log t +
C.

Int f(x) dx = log (arctan x) +
C.