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Math Help - Integration help please these are three small even basic integration problems

  1. #1
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    Integration help please these are three small even basic integration problems

    Integrate x(f(x))6 dx, using the substitution u = f(x).( where f(x) is 9x^2 -4

    Integrate x+2/f(x) dx where f(x) is 9x^2 -4

    Integrate 1/(4-9x^2)^1/2 dx


    Please a step by step process is appreciated as I am horrible in integration and need help, Thank you for your help =)
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  2. #2
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    Quote Originally Posted by aa751 View Post
    Integrate x(f(x))6 dx

    I don't know what that "6" means
    , using the substitution
    u = f(x).( where f(x) is 9x^2 -4
    You are told= what to do- DO IT! Let u= 9x^2- 4. What is du?

    Integrate x+2/f(x) dx where f(x) is 9x^2 -4
    Is this x+ \frac{2}{f(x)} or \frac{x+ 2}{f(x)}?

    Integrate 1/(4-9x^2)^1/2 dx
    Think of " \sqrt{1- sin^2(x)}= cos(x)". Try 3x= 2sin(u).


    Please a step by step process is appreciated as I am horrible in integration and need help, Thank you for your help =)
    Last edited by mr fantastic; November 2nd 2010 at 03:05 PM. Reason: Fixed quote tag.
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  3. #3
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    x(f(x))^6 dx thats what I meant sorry
    the second question is actually Integrate (x+2)/f(x) sx where f(x)= 9x^2-4

    sorry about the misunderstanding

    I actually now understand the 1st and 2nd one but I still dont get the third one
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  4. #4
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    For the third one, use trigonometric substitution.

    \displaystyle \int \frac{1}{\sqrt{4-9x^2}}dx

    As HallsofIvy stated, let 3x= 2 \sin(u)
    Therefore dx = ... du

    Make that substitution then use trigonometric identities to simplify the square root.
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