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Math Help - How do you solve this integral?

  1. #1
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    How do you solve this integral?

    integral [ (x^3+4x^2-x+2)/(2x^4+5x^2+2) dx]

    I tried solving it by using partial fractions, but answer my answer doesn't match the one in the back of the book.

    I put it in the following format and attempted to solve for the constants.

    (Ax+B)/(2x^2+1)+(Cx+D)/(x^2+2)
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  2. #2
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    Hello,
    Quote Originally Posted by cityismine View Post
    integral [ (x^3+4x^2-x+2)/(2x^4+5x^2+2) dx]

    I tried solving it by using partial fractions, but answer my answer doesn't match the one in the back of the book.

    I put it in the following format and attempted to solve for the constants.

    (Ax+B)/(2x^2+1)+(Cx+D)/(x^2+2)
    Can you show your working so that we can check together what's wrong ?

    If you want to check, the partial fractions should be :

    \frac{x+2}{x^2+2}-\frac{x}{2x^2+1}
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  3. #3
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    Those are the exact fractions I got, I probably made a mistake integrating afterwards. Let me check my work...
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  4. #4
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    How do you integrate (x+2)/(x^2+2). I believe this is the step, that I'm having trouble with.
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  5. #5
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    Quote Originally Posted by cityismine View Post
    How do you integrate (x+2)/(x^2+2). I believe this is the step, that I'm having trouble with.
    \int{\frac{x+2}{x^2+2}}=\int{\frac{x}{x^2+2}} + 2\int{\frac{dx}{x^2+2}}
     <br />
=\frac{1}{2}\int{\frac{2x}{x^2+2}}+2\int{\frac{dx}  {x^2+(\sqrt{2})^2}}<br />
    now for the first integral just substitute t=x^2+2 and you're done, as for the second it's a tabular one!
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