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)-x)
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)-x)