Question

用部分积分法求下列不定积分:∫arccos xdx.

Answer 1

∫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