Posted by Daniel on .
Integral of 10 / (5x^2  2x^3) Do not determine the numerical values of the coefficients.
Just wanted to know why when I write out the form of the partial fraction decomposition
there is A/x + B/x^3 + C/ (x^2 + 4)
Why isn't it just A/x^3 + B/ (x^2 + 4)?

calculus 
Reiny,
your denominator is
5x^2  2x^3
= x^2(52x)
so you could have had 3 fractions,
A/x + B/x^2 + C/(52x)
that would have given you a LCD of x^2(52x)
or 5x^2  2x^3
I don't see how you got your choice or even the supposedly correct choice. 
calculus 
Daniel,
Sorry I typed out the wrong answer. Why would I have 3 fractions though? Because it's x^2?

calculus 
Reiny,
yes, the option I gave you was
A/x + B/x^2 + C/(52x)
of course it could have been only 2 fractions with
B/x^2 + C/(52x) , and the LCD would also have been
x^2(52x)
but we don't know that, so we have to take the worstcase scenario.