Замена t=arctg[x^(1/2)]
dt=darctg[x^(1/2)]=1/(1+[x^(1/2)]^2) * 1/(2x^(1/2)) * dx =
=dx/(2x^(1/2) (1+x)) ==> dx/(x^(1/2) (1+x)) = 2dt
получаем интеграл int(t*2dt)