## anonymous one year ago How to solve following integration (5x^2-1)/ x(x-1)(X+1 dx

1. 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

2. anonymous

Thanks Castiel. I will try and shall get back. Wondering A/x is permissible?

3. IrishBoy123

$\frac{5x^2-1}{x(x-1)(x+1)}$

4. anonymous

IrisBoy- you are right. Pl suggest how to solve it.

5. anonymous

you can use partial fraction.

6. 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.

7. Jhannybean

Oh!! what if you expanded the base and then used long division or synthetic division to simplify it a bit?

8. Jhannybean

$$(x(x-1)(x+1)) = x(x^2-1) = x^3 - x$$

9. anonymous

$\frac{ 5x^2-1 }{ x(x-1)(x+1)}=\frac{ 2 }{ (x-1) }+\frac{ 2 }{ (x+1) }+\frac{ 1 }{ x}$

10. anonymous

11. anonymous

Great