How to integrate (x^2+1)^2/(x^2+1)?

The integral of (x^2+1)^2/(x^2+1) is x^3/3 + x + C.

To integrate (x^2+1)^2/(x^2+1), we can simplify the expression by cancelling out the common factor of (x^2+1) in the numerator and denominator. This gives us:

∫(x^2+1)^2/(x^2+1) dx = ∫(x^2+1) dx

Expanding the brackets, we get:

∫(x^2+1) dx = ∫x^2 dx + ∫1 dx

Integrating each term separately, we get:

∫x^2 dx = x^3/3 + C1

∫1 dx = x + C2

Therefore, the final answer is:

∫(x^2+1)^2/(x^2+1) dx = x^3/3 + x + C

where C is the constant of integration.