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# Integration watch

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1. Hi there.
I'm stuck in this qustion

I'm having trouble working out the values of a,b,c,d.

I did:
(ax+b)(x^2-2x+2)+(cx+d)(x^2+2x+2)≡1
and got when x=0
(i) 2b+2d≡1
(ii)a=-c;
(iii)-2a+b+2c+d≡0;
(iv)2a-2b+2c+2d≡0

so c=-1/8; a=1/8
d=b=1/4

This doesn't seem right because i need to integrate the two fractions and it doesn't work.

Thanks.
2. (Original post by Goldenratio)
Hi there.
I'm stuck in this qustion

I'm having trouble working out the values of a,b,c,d.

I did:
(ax+b)(x^2-2x+2)+(cx+d)(x^2+2x+2)≡1
and got when x=0
(i) 2b+2d≡1
(ii)a=-c;
(iii)-2a+b+2c+d≡0;
(iv)2a-2b+2c+2d≡0

so c=-1/8; a=1/8
d=b=1/4

This doesn't seem right because i need to integrate the two fractions and it doesn't work.

Thanks.
You can integrate the LHS whatever a,b,c,d are.

Make a sub of u = x+1 in the left fraction and v = x-1 in the right and it might become clearer.
3. Thanks!
Sorry I'm not seeing it.
4. (Original post by Goldenratio)
Thanks!
Sorry I'm not seeing it.
(ax+b)/(x^2+2x+2) becomes

au/(u^2+1) + (b-a)/(u^2+1)

which are standard integrals.
5. How did you split the fraction? Obviously there arent any factors so...
It's a STEP ii question, but i'm just not getting there.
Thanks
6. Why couldn't I integrate the 1/(x^4+4) by substituting x^2=2tan^2p?
7. (Original post by Goldenratio)
How did you split the fraction? Obviously there arent any factors so...
What do you mean? They split the fraction for you

I just made the u = x+1 sub I'd previously suggested.
8. Okay thanks, got you!

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