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Math Help - MIT integration bee questions

  1. #1
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    MIT integration bee questions

    #1

    [3x^3 -9]^(1/2)
    ______________
    x

    #2

    [8x+6x^(5/2)]^(1/2)

    I think we need to use substitution to solve these....anybody?
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  2. #2
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    Quote Originally Posted by mag6 View Post
    #1

    [3x^3 -9]^(1/2)
    ______________
    x

    #2

    [8x+6x^(5/2)]^(1/2)

    I think we need to use substitution to solve these....anybody?

    The first one , substitute  x^3 = t

    The second one , first let  x = t^2 then let  t^3 = u or you just let  x = u^{\frac{2}{3} }
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  3. #3
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    Quote Originally Posted by simplependulum View Post
    The first one , substitute  x^3 = t

    The second one , first let  x = t^2 then let  t^3 = u or you just let  x = u^{\frac{2}{3} }
    nope.....that's not working....none of them.

    i tried taking u= x^3 - 3 in the first one but that's not working either.
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  4. #4
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    For the first one, do s=\sqrt{3x^3-9}. For the second, s=6x^{3/2}+8.
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  5. #5
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    Quote Originally Posted by maddas View Post
    For the first one, do s=\sqrt{3x^3-9}. For the second, s=6x^{3/2}+8.
    how did you figure that out?!?! both of them are correct.....
    how do you integrate them further?
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  6. #6
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    Note that they're both essentially what simplependulum said, followed up by one more substitution.
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