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Integral of (sin (x))^1/2)(cos^3(x)) dx

  1. Feb 15, 2006 #1
    Not really sure where to begin on this integral. Hope this reads alright on here.

    Integral of (sin (x))^1/2)(cos^3(x)) dx
     
  2. jcsd
  3. Feb 15, 2006 #2
    [tex] \int {\sqrt{sin(x)}} cos(x)^3 dx [/tex]

    Convert this into

    [tex] \int {\sqrt{sin(x)}}cos^2(x)cos(x) [/tex].

    From your identities in trignometry

    [tex] cos^2(x) = 1 - sin^2(x) [/tex].

    This will leave you with all sine terms and one cosine term once you rewrite cosine squared. Do you see what to do from here?
     
    Last edited: Feb 15, 2006
  4. Feb 15, 2006 #3
    That was very helpful, thank you. Could I also get help with this one pls? :) I just seem to have a hard time figuring out where to start on these.

    The integral of (sin(ln x))/x dx
     
  5. Feb 15, 2006 #4
    Use a substitution letting u = ln x.
     
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