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Basic Integration

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data
    evaluate the integral.

    2. Relevant equations
    [itex]\int (cotx)[ln(sinx)] dx[/itex]

    how would i do this using basic integration techniques from calculus 1? i am not allowed to use, int by parts, partial fractions, trig sub, etc..

    3. The attempt at a solution
    i tried doing a u=sinx but don't know how to get the cotx.
     
    Last edited: Mar 14, 2013
  2. jcsd
  3. Mar 14, 2013 #2

    SammyS

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    Where's the "dx" ?

    [itex]\displaystyle \int \cot(x)\ln(\sin(x))\,dx[/itex]

    This may help. [itex]\displaystyle \ \cot(x)=\frac{\cos(x)}{\sin(x)}[/itex]
     
  4. Mar 14, 2013 #3
    thanks.

    so i have:

    u=sinx; du=cosx

    [itex]\int \frac{ln(u)}{u} du[/itex]

    v=lnu; dv=(1/u) du

    [itex]\int v dv[/itex] = [itex]\frac{v^2}{2}[/itex] = [itex]\frac{(lnu)^2}{2}[/itex]

    = [itex]\frac{[ln(sinx)]^2}{2}[/itex]
     
  5. Mar 14, 2013 #4
    Looks good to me, other than the +C.
     
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