How to solve following integration
(5x^2-1)/ x(x-1)(X+1 dx

Question

How to solve following integration
(5x^2-1)/ x(x-1)(X+1 dx

castiel · Answer

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 · Answer

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

irishboy123 · Answer

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

anonymous · Answer

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

anonymous · Answer

you can use  partial fraction.

jhannybean · Answer

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 · Answer

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

jhannybean · Answer

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

anonymous · Answer

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

anonymous · Answer

attachment

anonymous · Answer

Great