anonymous
  • anonymous
How to solve following integration (5x^2-1)/ x(x-1)(X+1 dx
Mathematics
jamiebookeater
  • jamiebookeater
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Castiel
  • Castiel
This looks like it need to be first separated with partial fractions and then you integrate all the pieces you get. It's that thing ....=A/x + B/(x-1) + C(x+1), you get A, B and C and you have much simpler integration
anonymous
  • anonymous
Thanks Castiel. I will try and shall get back. Wondering A/x is permissible?
IrishBoy123
  • IrishBoy123
\[\frac{5x^2-1}{x(x-1)(x+1)}\]

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anonymous
  • anonymous
IrisBoy- you are right. Pl suggest how to solve it.
anonymous
  • anonymous
you can use partial fraction.
Jhannybean
  • Jhannybean
Since you're got x, x-1 and x+1 in the DENOMINATOR, you know that somewhere you'll simplify this to a function of logs! If that helps.
Jhannybean
  • Jhannybean
Oh!! what if you expanded the base and then used long division or synthetic division to simplify it a bit?
Jhannybean
  • Jhannybean
\((x(x-1)(x+1)) = x(x^2-1) = x^3 - x\)
anonymous
  • anonymous
\[\frac{ 5x^2-1 }{ x(x-1)(x+1)}=\frac{ 2 }{ (x-1) }+\frac{ 2 }{ (x+1) }+\frac{ 1 }{ x}\]
anonymous
  • anonymous
anonymous
  • anonymous
Great

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