## anonymous 5 years ago ∫x+1/2x-x2+2 dx

1. anonymous

Pls guys help me solve this problem i have Exams tomorrow. pls

2. anonymous

do you know how to long divide polynomials?

3. anonymous

yes

4. anonymous

That's pretty much what you have to do here, so that your integral becomes (-x+3) - (1/(x+1)). Then you can solve the integral.

5. anonymous

hold up a minute, I think I messed it up, give me a minute or two.

6. anonymous

ok

7. anonymous

the denominator is 2x-x square + 2

8. anonymous

it looks like you separate by partial fractions $x+1 =( Ax +B)/(2x-x^2+2)$. Because the deonimator is a irreducible quadratic eq. Once you solve for A and B, then you should have a differentiable eq.

9. anonymous

sorry about the mix up before I jumped into a bad conclusion too fast.

10. anonymous

$\int\limits \left(2+\frac{1}{2 x}+x-x^2\right) \, dx = 2 x+\frac{x^2}{2}-\frac{x^3}{3}+\frac{\text{Log}[x]}{2}$

11. anonymous

hello

12. anonymous

is that the final ans.

13. anonymous

from robtobey, Yes. Another version is the result factored: $\frac{1}{6} \left(12 x+3 x^2-2 x^3+3 \text{Log}[x]\right)$

14. anonymous

You can check the result of the integration by taking the derivative of the result with respect to x.