Tricky partial fractions / integral lab problem

[tblaze]

The integral of ((x^4)+(18x^2)+x+80) / ((x-1)((x^2+9)^2))

I decomposed it yielding:

(A/x-1) + ((Bx+C)/(x^2+9)) + ((Dx+E)/((x^2+9)^2))

then I factored the xs out and distributed.
now I have 5 equations:

A + B = 1
-B + C = 0
18A + 9B - C + D = 18
-9B + 9C - D + E = 1
81A - 9C - E = 80

I got really big numbers like:
A= 100
B = -99
C = -99
...

while wolfram got:
A = 1
B = 0
C = 0
D = 0
E = 1


not sure what I'm doing wrong....

 

[stapel]

The integral of ((x^4)+(18x^2)+x+80) / ((x-1)((x^2+9)^2))

I decomposed it yielding:

(A/x-1) + ((Bx+C)/(x^2+9)) + ((Dx+E)/((x^2+9)^2))

then I factored the xs out and distributed.
now I have 5 equations:

A + B = 1
-B + C = 0
18A + 9B - C + D = 18
-9B + 9C - D + E = 1
81A - 9C - E = 80

I got really big numbers like:
A= 100
B = -99
C = -99
...

while wolfram got:
A = 1
B = 0
C = 0
D = 0
E = 1

not sure what I'm doing wrong....

Until we can see your steps, I'm afraid there's no way for us to advise where things may have gone wrong. Sorry.

 

[tblaze]

it is all good! me and a friend worked it out!