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Math Help - ıntegralllll questions

  1. #1
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    ıntegralllll questions

    3) INT(3x^2 + 3)/[(x-1)^3](x^2 + 1)dx???




    4) INT(sinx)/[(cos^3(2x))^1/2]dx???
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  2. #2
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    Quote Originally Posted by berkanatci View Post
    3) INT(3x^2 + 3)/[(x-1)^3](x^2 + 1)dx???




    4) INT(sinx)/[(cos^3(2x))^1/2]dx???
    This one is easy:
    INT (3x^2 + 3)/[(x-1)^3(x^2 + 1)] dx

    We need to use "Partial Fractions"
    INT [A/(x - 1) + B/(x - 1)^2 + C/(x - 1)^3 + (Dx + E)/(x^2 + 1)] dx

    Now we need to find the values of A, B, C, D, and E.
    A(x - 1)^2(x^2 + 1) + B(x - 1)(x^2 + 1) + C(x^2 + 1) + (Dx + E)(x - 1)^3 = 3x^2 + 3

    Multiply all of that out, and match up the x^4, x^3, x^2, x and constant terms. Set the sum of coresponding terms to the following:
    {x^4 terms} = 0
    {x^3 terms} = 0
    {x^2 terms} = 3x^2
    {x terms} = 0
    {constants} = 3

    This represents a system of equations, which you can use to solve for A, B, C, D, and E. Once you have these, solve the integration:
    INT [A/(x - 1) + B/(x - 1)^2 + C/(x - 1)^3 + (Dx + E)/(x^2 + 1)] dx
    Which at this point, should be much easier to do.
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  3. #3
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    I have a problem solving this........
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