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Integration by substitution

  1. Oct 20, 2006 #1
    evaluat the indefinite integral ((sin(x))/(1+cos^2(x)))dx

    I let

    u = 1 + cos^2(x)

    then du = -sin^2(x)dx

    I rewrite the integral to

    - integral sqrt(du)/u

    can I set it up like this? should I change u to something else?

    I also tried it like this by rewriting the original equation to:

    indefinite integral ((sin(x))/(1+cos(x)cos(x)))dx

    u = cos(x)

    du = -sin(x)dx

    then

    - integral (du)/(1+(u^2))

    Also, can somebody give me directions on how to format equations in this message board to make my questions somewhat clearer.


    Thanks alot!
     
  2. jcsd
  3. Oct 20, 2006 #2
    That's not right. The derivative of [tex]\cos^2{x}[/tex] is NOT [tex]-\sin^2{x}[/tex].

    Yes you can. The final integral is pretty straightforward.

    Download the pdf docs here
    https://www.physicsforums.com/showthread.php?t=8997
     
  4. Oct 20, 2006 #3
    neutrino's right - you can't differentiate [tex]\cos^2{x}[/tex] as [tex]-\sin^2{x}[/tex]. If it helps, think of [tex]\cos^2{x}[/tex] as [tex]cos{x} * cos{x}[/tex]. You can then use the chain rule.
     
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