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Math Help - Partial Fractions of integral (10x+2)/(x^3-5x^2+x-5)

  1. #1
    Junior Member
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    Partial Fractions of integral (10x+2)/(x^3-5x^2+x-5)

    Problem:
    \int\frac{10x+2}{x^3-5x^2+x-5}dx

    Attempt:
    Hint: x^3 - 5x^2 + x -5 = x^2(x-5) + x - 5

    Can someone tell me how to use partial fractions when there is addition and subtraction in the denominator. My book only covers multiplication. Do I have to use trig substution?

    Correct Answer:
     <br />
2ln(x-5)-ln(x^2+1)+C<br />
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Look at your hint:



    =(x^2+1)(x-5)
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