设 u=arctan [x^(1/2)],
则du =(1/2)x^(-1/2)/ (1+x)

∫arctan [x^(1/2)] / [ (1+x) x^(1/2) ]dx = ∫ 2udu =u^2 + C
= { arctan [x^(1/2)] }^2 + C