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    Hi please could someone help with exercise 4.1 part b)? I've got the denominator factorised as x(x^2+2x+5) but not sure how to split the fraction into partial fractions.
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    (Original post by jordanwu)
    Hi please could someone help with exercise 4.1 part b)? I've got the denominator factorised as x(x^2+2x+5) but not sure how to split the fraction into partial fractions.
    So it would be in the form \displaystyle \frac{A}{x}+\frac{Bx+C}{x^2+2x+5  }
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    (Original post by TeeEm)
    A/x +(Bx + C)/(x^2+2x+5), as the denominator is irreducible
    I ended up with -1/x + 4x/x^2+2x+5, where should I go on from here?
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    (Original post by jordanwu)
    I ended up with -1/x + 4x/x^2+2x+5, where should I go on from here?
    Integrate the first fraction which should be straightforward.

    Then if you express the second one as:

    \displaystyle 2\int \frac{2x}{x^2+2x+5}.dx =2\int \frac{(2x+2)-(2)}{x^2+2x+5}.dx

    \displaystyle =2\int \frac{2x+2}{x^2+2x+5}.dx + 2\int \frac{-2}{x^2+2x+5}.dx

    which is straight forward as well.
 
 
 
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