Friday, 22 November 2019

calculus - Not able to solve intlimitsn1fracg(x)xp+1mathrmdx



If p=78 then what should be the value of n1g(x)xp+1dx
when g(x)=xlogxorg(x)=xlogx?



Wondering which way to proceed?




  1. an algebraic substitution,

  2. partial fractions,


  3. integration by parts, or

  4. reduction formulae.



Please don't suggest something like ("Learn basic Calculus first" etc).
Kindly help by solving if possible because I'm out of touch with calculus for nearly 15 yrs.


Answer



g(x)xp+1=xlogxxp+1=logxxp



By parts:




u=1xp,u=pxp+1v=logx,v=xlogxx



Thus:



n1logxxpdx=(logxxp11xp1)|n1+pn1logxxpdxpn11xpdx


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