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Math Help - trying to slove ıntegration

  1. #1
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    trying to slove ıntegration

    1) INT dx/[x[(4+x^2)^2](1+x^2)]??????




    2) INT [X/(X^2 +6X+3)]^2dx??????
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by berkanatci View Post
    1) INT dx/[x[(4+x^2)^2](1+x^2)]??????




    2) INT [X/(X^2 +6X+3)]^2dx??????
    1) INT 1/[x[(4+x^2)^2](1+x^2)] dx

    On an earlier problem (on one of the other posts) I explained how to use "Partial Fractions" to solve a particular integration. This one involves the same principle:

    Set up the Partial Fractions as:
    INT [ A/x + (Bx + C)/(4 + x^2) + (Dx + E)/(4 + x^2)^2 + (Fx + G)/(1 + x^2) ] dx

    Find the common denominator for each and add the terms to get the following numerator:
    A(4 + x^2)^2*(1 + x^2) + (Bx + C)(x)(4 + x^2)(1 + x^2) + (Dx + E)(x)(1 + x^2) + (Fx + G)(x)(4 + x^2)^2

    That's a lot to multiply out, but it can be done (and I don't feel like doing it ). Once you get it done, you'll have a bunch of terms of the following forms: x^6, x^5, x^4, x^3, x^2, x, and Constants. Set the sums of those terms equal to the following:
    {terms of x^6} = 0
    {terms of x^5} = 0
    {terms of x^4} = 0
    {terms of x^3} = 0
    {terms of x^2} = 0
    {terms of x} = 0
    {constants} = 1

    Then solve for each letter, and use those to solve the above integration (using whatever method is necessary). That's just too much work to type up... so I won't do it unless you specifically ask.
    Last edited by ecMathGeek; March 29th 2007 at 07:25 AM.
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  3. #3
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    thank u so much

    I have many problems and I have to solve 140 questions which my math teacher gave to me

    My exam ll be started 6 april

    If I pass the exam,I ll be so happy that nobody understands me
    thanks to u .)):
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