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Integrate sinx*sqrt(1+((cosx)^2))dx

  1. Feb 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Integrate sinx*sqrt(1+((cosx)^2))dx


    2. Relevant equations
    integral udv = uv - integral vdu


    3. The attempt at a solution
    I tried integration by parts which is: integral udv = uv - integral vdu
    I tried substituting (cosx)^2= 1-(sonx)^2
    neither of them seemed to work...
     
  2. jcsd
  3. Feb 8, 2009 #2
    Oops, bad advice. Sorry
     
  4. Sep 3, 2009 #3
    Hi, the your integrated is resolved by wolframalpha.com.
    Here's the image:

    << Complete solution removed by Hootenanny >>
     
  5. Sep 3, 2009 #4
    Use the substitution tan(x) = t

    [tex]sin^2(x)=\frac{tan^2(x)}{1+tan^2(x)}=\frac{t^2}{1+t^2}[/tex]

    [tex]cos^2(x)=\frac{1}{1+tan^2(x)}=\frac{1}{1+t^2}[/tex]

    [tex]dx=\frac{dt}{1+t^2}[/tex]

    Or even better, you can use the substitution cos(x)=t
     
  6. Sep 3, 2009 #5
    You could also use the substitution u = cosx. Then your integral turns into [tex] - \int \sqrt[]{1+u^2} du [/tex].

    Do you recognize this integral now?
     
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