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Question

Integrate the function w.r.t x : x(logx)2

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Solution

Putting logx=m
dxx=dm
dx=emdm
m2e2mdm
Integrating by parts we get,
u=m2,v=e2m
u=2m,vdm=12e2m
m2e2m2me2mdm
Again integrating by parts
u=m,v=e2m
u=1,vdm=e2m2
m2e2m2me2m2+e2m4
(logx)2x22x2logx2+x24


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