Tuesday, 26 May 2015

calculus - Evaluate int10frac(x21)logxdx




Evaluate10(x21)logxdx



Context:



I came across a similar integral some time ago, and now I would like to know how to tackle this. Any hint is very welcome.


Answer



Let f(k)=10xk1logxdx



Then f(k)=10xklogxlogxdx=10xkdx=11+kf(k)f(0)=log(1+k)f(k)=log(1+k)




Evaluating k=2 we get f(2)=10x21logxdx=log(1+2)=log3


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