求∫（arcsinx)^2dx=?

令arcsinx=t x=sint ∫（arcsinx)^2dx =∫t^2costdt =∫t^2dsint =t^2sint-2∫tsintdt =t^2sint+2∫tdcost =t^2sint+2(tcost-∫costdt) =t^2sint+2(tcost-sint) ∫（arcsinx)^2dx=x(arcsinx)^2+2(arcsinxcos(arcsinx...