∫arccosxdx
=xarccosx-∫xd(arccosx)
=xarccosx+∫xdx/√(1-x²)
=xarccosx+(1/2)∫d(1-x²)/√(1-x²)
=xarccosx+(1/2)∫[(1-x²)^(-1/2)]d(1-x²)
=xarccosx+√(1-x²)+C