Question

ʃ dx/x^4(1/x^2-2)^2

please help i need solution..i got the answer..
answer= 1/6(1-2x^3)=c

thanks

Answer 1

Differentiating your answer would give us
x^2 , not anywhere near your starting integral.
You should have realized that your answer cannot be correct.

Before any tutor starts your messy expression, we cannot tell exactly what you mean
According to the way you typed it and following the order of operation I read that as

ʃ (1/x^4)(1/x^2-2)^2 dx

please confirm

Answer 2

(1/x^4)(1/(x^2-2))^2 dx
= (x^2 - 2)^2/x^4
= (x^4 - 4x^2 + 4)/x^4

That's just a bunch of power terms x^n.

As Reiny said, please clarify what your expression really is.

note that 1/x^2-2 can be (1/x^2) - 2 or (1/(x^2 - 2) depending on how casual you are in your use of parentheses.