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Past exam of the options II course of the University of Oxford / 2009 / D / D3 / ii / a / Solution

Codex (@codex,  0) ... Past exam of the options II course of the University of Oxford 2009 D D3 ii a
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The function is measurable and negative on this interval. Its absolute value obeys
0≤(1+x)2−xlogx​≤−xlogx,∫01​−xlogxdx=41​.
(1)
The final integral follows by integration by parts and x2logx→0 at zero. The comparison test for integrals proves integrability.

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