Final answer:
The expression x² - 4 / x² simplifies to 1 - 4/x², which can then be integrated term by term to give the result x - 4/x + C'', with C'' representing the integration constant.
Step-by-step explanation:
To solve the given equation x2 - 4/x2, we can simplify the expression by dividing the numerator by the denominator. We get:
(x2 - 4) / x2 = x2/x2 - 4/x2 = 1 - 4/x2
Now we further simplify the expression by realizing that 4/x2 is the square of (2/x), so we have:
1 - (2/x)2
This equation can now be integrated term by term:
- ∫ dx = x + C
- -∫ (2/x)2 dx = -∫ 4/x2 dx = -4/x + C'
Combining both integrals, we have:
x - 4/x + C''
Where C'' is the combination of both constants of integration.