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Partial Fractions

  1. Feb 20, 2008 #1
    Integrate using partial fractions:

    (int) (x^3)/(x^2 -1) dx

    I have put into the form (int) (x^3)/((x-1)(x+1)) dx

    I thought partial fractions had this property:

    'Partial fractions can only be done if the degree of the numerator is strictly less than the degree of the denominator.'

    And this obviously doesn't, so how do you do it?
  2. jcsd
  3. Feb 20, 2008 #2


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    Divide! What is x3 divided by x2- 1? What are the quotient and remainder?
  4. Feb 20, 2008 #3

    so it =

    x + 1/(x-1) - 1/(x+1)(x-1)

  5. Feb 20, 2008 #4
    While im here I have another question:

    (int) 1 to e (ln(x))/x^2 dx

    THe question says, use a suitable substitution to evaluate the definite integral, I can do it by parts but I don't want to lose marks for it.

    Can any1 suggest the substitution to get me started?
  6. Feb 20, 2008 #5
    This should be in the Calculus section.

    Verifying your problem ...

    [tex]\int_1^e\frac{\ln x}{x^2}dx[/tex]
  7. Feb 20, 2008 #6
    Yep that's the one
  8. Feb 20, 2008 #7
    Substitutions ...

    [tex]t=\ln x \rightarrow e^t=x[/tex]

    [tex]dt=\frac 1 x dx[/tex]

    You will need to do parts afterwards.
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