Question

求下列不定积分(求解题过程)

求下列不定积分(求解题过程)求下列不定积分(求解题过程)

Answer 1

如图

追答

Answer 2

😁

追答

∫xcosxdx
=∫xdsinx
=xsinx-∫sinxdx
=xsinx+cosx

原式=∫x²dsinx
=x²sinx-∫sinxdx²
=x²sinx-2∫xsinxdx
=x²sinx+2∫xdcosx
=x²sinx+2xcosx-2∫cosxdx
=x²sinx+2xcosx-2sinx+C

解：令 ∫ e^xcosx dx = A
A = ∫ e^x cosx dx
= ∫ cosx de^x
= e^x cosx - ∫ e^x dcosx
= e^x cosx + ∫ e^x sinx dx
= e^x cosx + ∫ sinx de^x
= e^x cosx + e^x sinx - ∫ e^x dsinx
= e^x cosx + e^x sinx - ∫ e^xcosx dx
= e^x cosx + e^x sinx - A
A = (e^x cosx + e^x sinx) / 2