如图
令lnx=t,则x=e^t,原=∫costdet=cost e^t-∫e^tdcost=cost e^t+∫e^tsintdt=cost e^t+∫sintde^t=cost e^t+e^tsint-∫e^tcostdt然后移项整理得原式=1/2(cost e^t+e^tsint)
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