## anonymous 3 years ago Evaluate the Intergal

1. anonymous

$\int\limits_{}^{}\frac{ 2x^4-4x^3+13x^2-6x+10 }{ (x-2)(x^2-2x+5)^2 }dx$

2. anonymous

I solved it using a beastly amount of partial fractions after solving a system of 5 equations. Please tell me there is another easier way.

3. anonymous

jus divide the numerator by x-2

4. anonymous

Why though? I have no reason to do long division.

5. anonymous

it is jus to simplify the question

6. anonymous

Hmm Okay... Let me see...

7. anonymous

Yep. it simplifies, reducing your amount of work.

8. anonymous

ok, maybe not. I really need a break. Making too many mistakes today. See you all later.

9. anonymous

Erm... THat doesent help O_o . I get: $2x^3+13x+20 +\frac{ 50 }{ 2x^3+13x+20 }$

10. anonymous

no it doesn't simplify but it has been cooked so that the partial fractions are nice integers

11. anonymous

yeah ^ he's right

12. anonymous

Ohh they are nice and all but even evaluating the damn partial fractions takes forever.

13. anonymous

there are some snap methods for getting some of them i think eliasaab who i have not seen here for a while had a snappy way of doing it

14. anonymous

So after the decomposition I get: $\int\limits_{}^{}\frac{ 2 }{ x-2 }+\frac{ 4 }{ x^2-2x+5 }+\frac{ x }{ (x^2-2x+5)^2 }dx$

15. anonymous

The first term is fine. It's the other two that take forever to integrate.

16. anonymous

all integration is a useless pain in the butt that is why they invented computers it is not math, it is wasted doodling

17. anonymous

Wolfram made I think... 9 substitutions. I refuse to do that.

18. TuringTest

@satellite73 D: blasphemy, integration is an art form!

19. anonymous

art who?

20. anonymous

waste a bunch of time showing off, saying "oh look, can find a function whose derivative is this, and a function whose derivative is that" when the truth is that if you pick a function out of a hat the probability you can find a nice closed for for the anti derivative is zero!

21. anonymous

I mean I got the correct answer. But isn't there an easier way to do this?

22. anonymous

23. anonymous

Damn it. Thanks anyways guys :)

24. TuringTest

haha, true that. PF is just plain annoying