∫xln2xdx=________.

admin2021-10-18  31

问题 ∫xln2xdx=________.

选项

答案x2/2ln2x-1/2x2lnx+1/4x2+C

解析 ∫xln2xdx=1/2∫ln2xd(x2)=x2/2ln2x-1/2∫x2·2lnx/xdx=x2/2ln2xdx-∫xlnxdx=x2/2ln2x-1/2∫lnxd(x2)=x2/2ln2x-1/2(x2lnx-∫xdx)=x2/2ln2x-1/2x2lnx+1/4x2+C.
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