11—14题,高数,用分部积分法,

11—14题,高数,用分部积分法,

11：令lnx=t 则x=e^t 原式=∫sintde^t=sint*e^t-∫e^tcostdt=sint*e^t-∫costde^t=sint*e^t-cost*e^t+∫e^tdcost=sint*e^t-cost*e^t-∫sinte^tdt=sint*e^t-cost*e^t-∫sintde^t原式=(sint*e^t-cost*e^t)/2+C=[sin(lnx)*x-cos(lnx)*x]/2+C12：原式=∫x^2sin2xdx-∫sin2xdx=-1/2∫x^2dcos2x+1/2cos2x=-1/2x^2cos2x+1/2cos2x+1/2∫cos2xdx^2=-1/2x^2cos2x+1/2cos2x+∫xcos2xdx=-1/2x^2cos2x+1/2cos2+1/2∫xdsin2x=-1/2x^2cos2x+1/2cos2x+1/2xsin2x-1/2∫sin2xdx=-1/2x^2cos2x+1/2cos2x+1/2xsin2x+1/4cos2x+C13：令x^(1/2)=t 则x=t^2 原式=∫e^tdt^2=2∫te^tdt=2∫tde^t=2te^t-2∫e^tdt=2te^t-2e^t+C=2x^(1/2)e^[x^(1/2)]-2e^[x^(1/2)]+C14：原式=2∫xdsin(x/2)=2xsin(x/2)-∫sin(x/2)dx=2xsin(x/2)+2cos(x/2)+C

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