Hello and thanks for a great forum.
I just need some feedback on my calculations.
I need to integrate this 1/x^2(1+x)(1+x^2). Was thinking of doing it by factorisation. This is how a proceded.
Setting up the coefficients
A/x + B/x^2 + C/(1+x) + (Dx + E)/(1+x^2)
I multiply the eqvation with (1+x) and then put x = -1 to solve C
C = 1/-1^2(1+-1^2) C = 1/2
Once again a multiply with (1+x^2) to solve (Dx + E) and put x = i
Di + E = 1/i^2(1+i) Di + E = 1/(-1 – i) è D*1 + E = -1 – i
Is this correct so far,, im a bit uncertain when solving (Dx + E). Dont bother with A and B, I know how to solve them later on.
I really hate this method. Think about it.
1) Initially, the value you are about to substitue is NOT in the Domain.
2) If it IS in the Domain, you are about to multiply things by zero (0).
3) Why does this make sense?
On the other hand, one cannot deny that it works.
Your last trick shoud result in:
D + E = 0
D - E = 1
Solving the system produces the desired result.
Thank you for the help,, but im still a bit confused =P
So it should be like this afterwards.
A/x + B/x^2 + 1/2(1+x) - (Dx + E)/2(1+x^2)
C = 1/2
D = - 1/2
E = - 1/2
Did you get the small system in D and E? You must reproduce that, first. Then you shoudl get D = +1/2.
I think I got it now, thanks alot =)