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Math Help - need help with partial fraction

  1. #1
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    need help with partial fraction

    So we are having a holiday right now and I decide to go over the math which I'm bad at "partial fraction"

    The question is my exercise book is (x^3+3x+7)sin^2(y)\frac{dy}{dx}=x^2+1    for,         y(-1)=0

    so I work around with the algebra a bit and got the equation to become

    \int sin^2(y)dy=\int\frac{x^2+1}{x^3+3x+7}dx

    the problem is that I wasn't sure how to integrate \frac{x^2+1}{x^3+3x+7} this since I cannot factorise the denominator into somethign like (x^2+A)(x+B)
    so how does one set up \frac{x^2+1}{x^3+3x+7} for partial fractions


    Best Regards
    Junks
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  2. #2
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    Re: need help with partial fraction

    see the derivative of denominator is 3x^2 + 3 = 3(x^2+1) Thus you can write
    (x^2+1) / ( x^3 + 3x + 7 ) = 1/3 [ 3(x^2+1) + 7] /( x^3 + 3x + 7 )
    But still I observe that you will have a problem integrating 7 / ( x^3 + 3x + 7 )
    Thanks from junkwisch
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  3. #3
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    Re: need help with partial fraction

    Quote Originally Posted by junkwisch View Post
    So we are having a holiday right now and I decide to go over the math which I'm bad at "partial fraction"

    The question is my exercise book is (x^3+3x+7)sin^2(y)\frac{dy}{dx}=x^2+1    for,         y(-1)=0

    so I work around with the algebra a bit and got the equation to become

    \int sin^2(y)dy=\int\frac{x^2+1}{x^3+3x+7}dx

    the problem is that I wasn't sure how to integrate \frac{x^2+1}{x^3+3x+7} this since I cannot factorise the denominator into somethign like (x^2+A)(x+B)
    so how does one set up \frac{x^2+1}{x^3+3x+7} for partial fractions


    Best Regards
    Junks
    One probably wouldn't set it up for partial fractions. One would probably use u substitution.
    Thanks from junkwisch
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  4. #4
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    Re: need help with partial fraction

    Quote Originally Posted by SlipEternal View Post
    One probably wouldn't set it up for partial fractions. One would probably use u substitution.
    Thank you slipeternal

    I felt really dumb right now
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