Hello,

could someone tell me where I made a mistake on this partial fraction problem

Please

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- Feb 28th 2010, 07:22 AMwolfhoundIntegration partial fractions
Hello,

could someone tell me where I made a mistake on this partial fraction problem

Please - Feb 28th 2010, 07:32 AMArchie Meade
hi wolfhound,

$\displaystyle \frac{A}{x}+\frac{B}{x^2+1}=\frac{1}{x^3+x}$

$\displaystyle \frac{A\left(x^2+1\right)+Bx}{x\left(x^2+1\right)} =\frac{1}{x^3+x}$

$\displaystyle \frac{Ax^2+A+Bx}{x^3+x}=\frac{1}{x^3+x}$

$\displaystyle x\left(Ax+B\right)+A=x(0)+1$

$\displaystyle A=1$

$\displaystyle (1)x+B=0\ \Rightarrow\ B=-x$ - Feb 28th 2010, 07:39 AMwolfhound
Hi archie

Oh so I dont actually get a value for B? except B=-x?

someone said I should input*i*in to solve these also

when should I take a coefficient as x and not a value please? - Feb 28th 2010, 07:47 AMArchie Meade
Hi wolfhound,

sometimes there will be an x-component of the A and B values.

They are not necessarily "constants".

They are "numerators".

They only end up being constants sometimes.

If you add those two resulting fractions together,

you will see that the result is the original fraction you wanted to integrate.

since the sum of the resulting fractions is the original,

you can more conveniently integrate the partial fractions.

The trick is....

if the numerator of the original fraction is a constant,

then you can write it as "constant + (0)x" - Feb 28th 2010, 07:55 AMwolfhound
I see,

I am going to practice some more now

Thanks