## Dido525 Group Title Evaluate the Intergal one year ago one year ago

1. Dido525 Group Title

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

2. Dido525 Group Title

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. DHASHNI Group Title

jus divide the numerator by x-2

4. Dido525 Group Title

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

5. DHASHNI Group Title

it is jus to simplify the question

6. Dido525 Group Title

Hmm Okay... Let me see...

7. calmat01 Group Title

Yep. it simplifies, reducing your amount of work.

8. calmat01 Group Title

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

9. Dido525 Group Title

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

10. satellite73 Group Title

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

11. DHASHNI Group Title

yeah ^ he's right

12. Dido525 Group Title

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

13. satellite73 Group Title

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. Dido525 Group Title

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. Dido525 Group Title

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

16. satellite73 Group Title

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

17. Dido525 Group Title

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

18. TuringTest Group Title

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

19. satellite73 Group Title

art who?

20. satellite73 Group Title

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. Dido525 Group Title

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

22. satellite73 Group Title