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xsinxDx的值

∫xsinxdx=-∫xdcosx=-xcosx+∫cosxdx=-xcosx+sinx+C

积分上下限为π2和0,算式中没写,用分步积分:∫xsinxdx=∫xd(-cosx)=-xcosx-∫(-cosx)dx=sinx-xcosx=1

解:原式=-∫xd(cosx) =-xcosx+∫cosxdx (应用分部积分法) =-xcosx+sinx+c (c是积分常数).

分部积分法∫xsinxdx=-xcosx-∫-cosxdx=-xcosx+sinx+C

原式=∫-xd(cosx) =-xcosx+∫cosxd(-x) =-xcosx-∫cosxdx =-xcosx-sinx

用分部积分法:∫xsinxdx = -∫x(-sinx)dx = -∫xdcosx= -(xcosx - ∫cosxdx)= -(xcosx - sinx) + C= sinx - xcosx + C

∫xsinxdx=-xcosx+sinx+C

使用分部积分法,可以得到:=x*(-cosx) + ∫cosx*dx=-x*cosx + sinx + C

∫u(x)dv(x)=u(x) v(x)-∫v(x)du(x)∫xsin xdx=-∫xdcosxu(x)=x v(x)=-cosx所以∫xsin xdx=-∫xdcosx=-[-xcosx-∫cosxdx]=-[-xcosx-sinx+c]=xcosx+sinx+cc不分正负,最后只需+c

原式=-∫xd(cosx) =-xcosx+∫cosxdx (分部积分法) =-xcosx+sinx+C (C是积分常数).

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