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Math Help - A Few Integrals

  1. #1
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    A Few Integrals

    I'm stumped on these:

    The integral of x^3 (1+x^2)^3/2

    The integral of the square root of (x^2 - 1)dx/x^3

    The integral of x^3 dx/(4-x^2)^2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by GreySweatshirt306 View Post
    I'm stumped on these:

    The integral of x^3 (1+x^2)^3/2
    do a substitution, u = 1 + x^2

    The integral of the square root of (x^2 - 1)dx/x^3
    note that \frac {x^2 - 1}{x^3} = \frac {x^2}{x^3} - \frac 1{x^3} = \frac 1x - x^{-3}


    The integral of x^3 dx/(4-x^2)^2
    another substitution problem, let u = 4 - x^2
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  3. #3
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    Thanks for the help--but I don't see how a substitution works for either of those two problems.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by GreySweatshirt306 View Post
    Thanks for the help--but I don't see how a substitution works for either of those two problems.
    did you try it?

    \int {x^3}{(1 + x^2)^{3/2}}~dx

    Let u = 1 + x^2 \implies \boxed{x^2 = u - 1} ....note that x^3 = x \cdot x^2

    \Rightarrow du = 2x~dx

    \Rightarrow \frac 12 ~du = x~dx

    Thus our integral becomes

    \frac 12 \int \frac {u - 1}{u^{3/2}}~du

    i suppose you can take it from here. the other integral is similar
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  5. #5
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    Trig Substitution

    Is there anyway to do these using a trig sub?
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  6. #6
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    Utterly unnecessary.

    1) x=\tan\varphi.

    2) x=\sec\varphi.

    3) x=2\sin\varphi.
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  7. #7
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    Thanks

    Thanks for the help. I'm not very good at these though, could you flesh them out a bit? I really appreciate anything you can do
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by GreySweatshirt306 View Post
    Thanks for the help. I'm not very good at these though, could you flesh them out a bit? I really appreciate anything you can do
    what's wrong with the way they were done before? are you required to use trig subs?
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  9. #9
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    Yeah

    Trig Subs are required
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  10. #10
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    You didn't specify that from the beginning, and that's bad, pretty bad since you wasted Jhevon's time.

    If you want to be helped, show at least what you've tried.
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  11. #11
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    Well let me edit that--
    Trig subs are NOT required, what I meant to say is that I came to my math teacher with some of the work that Jhevon got me started on (thanks again), and he instructed me to also try to work them out using a trig substitution, so i'm back here. Sorry for the confusion
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