Evaluate the Intergal

Question

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

jus divide the numerator by x-2

anonymous · Answer

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

anonymous · Answer

it is jus to simplify the question

anonymous · Answer

Hmm Okay... Let me see...

anonymous · Answer

Yep. it simplifies, reducing your amount of work.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yeah ^ he's right

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

turingtest · Answer

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

anonymous · Answer

art who?

anonymous · Answer

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!

anonymous · Answer

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

anonymous · Answer

nope 
you can see that by how annoying your answer is

anonymous · Answer

Damn it. Thanks anyways guys :)

turingtest · Answer

haha, true that. PF is just plain annoying