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Math Help - Integration

  1. #1
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    Integration



    How do I even go about solving this? I get as far as u = x^4+1 and du = 4x^3
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  2. #2
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    what if you put t=x^2 ?
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  3. #3
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    Alright so I changed it so that it's u = x^2+1 and du = 2x dx.

    Eventually I get to 4 \int du * 1/u^2 and couldn't proceed.

    The du becomes x^2 but I don't know what to do with the second one. It could become arctan u, but the fact that it's 1/u^2 and not just 1/u prevents that from happening.
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  4. #4
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    no, actually your substitution won't work since you need to express x^4 in terms of your substitution and that is nasty.

    try my sub. and see what happens.
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  5. #5
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    Quote Originally Posted by Krizalid View Post
    what if you put t=x^2 ?
    What's t? du or u?
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  6. #6
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    it's any variable, that makes no difference.
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  7. #7
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    Alright so

    4 \int 2x/(x^4+1)
    u = x^2, du = 2x
    4 \int du/(u^2+1)

    Do I separate? Does it become 4 \int du * 1/(u^2+1)?

    In which case the answer should be 4 * x^2 * arctan x^2 + C, right?
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  8. #8
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    no, it's not the answer, but it's close.

    check your solution.
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  9. #9
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    I'm pretty sure I messed up on the du in the solution. But I don't understand... isn't that what it's supposed to be? du is 2x and when it's integrated it should become x^2.
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  10. #10
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    Quote Originally Posted by Archduke01 View Post
    I'm pretty sure I messed up on the du in the solution. But I don't understand... isn't that what it's supposed to be? du is 2x and when it's integrated it should become x^2.
    Once you get the integral to 4\int{\frac{1}{u^2 + 1}\,du} use the same trigonometric substitution I explained to you in another thread.
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