∫arctan√x dx

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∫arctan√xdx∫arctan√xdx∫arctan√xdx∫arctan√xdx令√x=t,x=t^2,dx=dt^2所以原式=∫arctantdt^2=t^2*arctant-∫t^2/(1

∫arctan√x dx
∫arctan√x dx

∫arctan√x dx
∫arctan√x dx
令√x=t,x=t^2,dx=dt^2
所以
原式=∫arctantdt^2
=t^2*arctant-∫t^2/(1+t^2)dt
=t^2*arctant-∫(t^2+1-1)/(1+t^2)dt
=t^2*arctant-t+arctant+c
=xarctan√x-√x+arctan√x+c