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The original formula = ∫ (1, e) lnxdx =xlnx(1,e)-∫(1,e)xdlnx =xlnx(1,e)-∫(1,e)x*1/xdx =xlnx(1,e)-∫(1,e)dx =(xlnx-x)(1,e) =(e-e)-(0-1) =1
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