∫ (ln√x)^2 dx
换元t=ln√x，e^t=√x，x=e^(2t)
=∫ t^2 d(e^(2t))
=t^2*e^(2t) - ∫ e^(2t) d(t^2)
=t^2*e^(2t) - 2*∫ e^(2t)*t dt
=t^2*e^(2t) - ∫ t*2*e^(2t) dt
=t^2*e^(2t) - ∫ t d(e^(2t))
=t^2*e^(2t) - t*e^(2t) + ∫ e^(2t) dt
=t^2*e^(2t) - t*e^(2t) + (1/2)*∫ 2*e^(2t) dt
=t^2*e^(2t) - t*e^(2t) + (1/2)*e^(2t) + C
=e^(2t) * (t^2-t+1/2) + C
=x * ((ln√x)^2-(ln√x)+1/2) + C
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