anonymous 5 years ago Find the integral:

1. anonymous

t^2 + 4 / t^3 +12t +8 dt

2. anonymous

Do you know how an integral works?

3. anonymous

They confuse me.

4. anonymous

Is it $\int\limits_{}^{}{t^2+4 \over t^3+12t+8} dt?$

5. anonymous

@AnwarAL it is what you posted. I think you can do u-substition for the integral.

6. anonymous

OK let's call the integral I .. if you look closely you will see that The numerator is the derivative of the denominator after multiplying it (The numerator) by 3.. SO, multiply The numerator by 3 and divide outside the integral by 3, you get: $I={1 \over 3}\int\limits_{}^{}{3t^2+12 \over t^3+12t+8}dt$ now you can see that The numerator is exactly the derivative of the numerator, then: $I={1 \over 3} \ln \left| t^3+12t+8 \right|+c$

7. anonymous

you can do substitution u=t^3+12t+8 as smorlaz said.. the way I used looks faster and easier to me. They both lead to the same result.

8. anonymous

does that make sense to you?

9. anonymous

Wait a minute, why can't you just seperate the terms and integrate individually?

10. anonymous

Or did I read the problem incorrectly?

11. anonymous

^^ I think you did :)