Hello,
could someone tell me where I made a mistake on this partial fraction problem
Please
hi wolfhound,
$\displaystyle \frac{A}{x}+\frac{B}{x^2+1}=\frac{1}{x^3+x}$
$\displaystyle \frac{A\left(x^2+1\right)+Bx}{x\left(x^2+1\right)} =\frac{1}{x^3+x}$
$\displaystyle \frac{Ax^2+A+Bx}{x^3+x}=\frac{1}{x^3+x}$
$\displaystyle x\left(Ax+B\right)+A=x(0)+1$
$\displaystyle A=1$
$\displaystyle (1)x+B=0\ \Rightarrow\ B=-x$
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"