Question

求：x^ 2cosx得不定积分

Answer 1

∫ x^2. cosx dx

=∫ x^2 dsinx

=x^2.sinx -2∫ xsinx dx

=x^2.sinx +2∫ x dcosx

=x^2.sinx +2xcosx -2∫ cosx dx

=x^2.sinx +2xcosx -2sinx +C

Answer 2

∫ x²cosx dx
= ∫ x² dsinx
= x²sinx - ∫ sinx dx²
= x²sinx - 2∫ xsinx dx
= x²sinx + 2∫ x dcosx
= x²sinx + 2xcosx - 2∫ cosx dx
= x²sinx + 2xcosx - 2sinx + C