- #1
clope023
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[SOLVED] integration by partial fractions
[tex]\int[/tex]((2x^2-1)/(4x-1)(x^2+1))dx
A1/ax+b + A2/(ax+b)^2 + ... + An/(ax+b)^n
(2x^2-1)/(4x-1)(x^2+1) = A/4x-1 + Bx+C/x^2+1
2x^2-1/x^2+1 = A + Bx+C(4x-1)/x^2+1
set x = 1/4, get
-14/17 = A + B(0), A = -14/17
I'm pretty much stuck here; I just need to get the values for B and C and I can solve it from there, any help is greatly appreciated.
Homework Statement
[tex]\int[/tex]((2x^2-1)/(4x-1)(x^2+1))dx
Homework Equations
A1/ax+b + A2/(ax+b)^2 + ... + An/(ax+b)^n
The Attempt at a Solution
(2x^2-1)/(4x-1)(x^2+1) = A/4x-1 + Bx+C/x^2+1
2x^2-1/x^2+1 = A + Bx+C(4x-1)/x^2+1
set x = 1/4, get
-14/17 = A + B(0), A = -14/17
I'm pretty much stuck here; I just need to get the values for B and C and I can solve it from there, any help is greatly appreciated.