∫arctan√xdx
=xarctan√x-∫x*1/[1+(√x)^2]*1/2*1/√xdx
=xarctan√x-1/2*∫√x/(1+x)*dx (令√x=t,则x=t^2,dx=2tdt)
=xarctan√x-1/2*∫t/(1+t^2)*2tdt
=xarctan√x-∫[1-1/(1+t^2)]dt
=xarctan√x-t+∫[1/(1+t^2)]dt
=xarctan√x-√x+arctan√x+C
=(x+1)arctan√x-√x+C
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