Solving an Integral: Struggling to Make Progress?

[tmt1]

I have this integral:

$$\frac {x^3 + 1}{x^2 - 4}$$

And I'm unsure how to approach it. I can factor the denominator like this $(x + 2)(x - 2)$ but I'm not sure if this is useful.

 

[mrtwhs]

\(\displaystyle \int \dfrac{x^3+1}{x^2-4} dx\)

Since the numerator has higher degree than the denominator, just do a long division. Once you've divided, you can do partial fractions or a trig substitution.

 

[soroban]

I have this integral:

$$\frac {x^3 + 1}{x^2 - 4}$$

And I'm unsure how to approach it.
I can factor the denominator like this $(x + 2)(x - 2)$
but I'm not sure if this is useful.

Use long divison and the integral becomes:. . $$\int \left(x + \frac{4x+1}{x^2-4}\right)dx$$

Then you can integrate these three integrals: .$$\int x\,dx + 4\int\frac{x\, dx}{x^2-4} + \int\frac{dx}{x^2-4}$$