Posted by **Daniel** on Saturday, March 2, 2013 at 3:14am.

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**, Saturday, March 2, 2013 at 8:28am
your denominator is

5x^2 - 2x^3

= x^2(5-2x)

so you could have had 3 fractions,

A/x + B/x^2 + C/(5-2x)

that would have given you a LCD of x^2(5-2x)

or 5x^2 - 2x^3

I don't see how you got your choice or even the supposedly correct choice.

- calculus -
**Daniel**, Saturday, March 2, 2013 at 3:30pm
Sorry I typed out the wrong answer. Why would I have 3 fractions though? Because it's x^2?

- calculus -
**Reiny**, Saturday, March 2, 2013 at 3:47pm
yes, the option I gave you was

A/x + B/x^2 + C/(5-2x)

of course it could have been only 2 fractions with

B/x^2 + C/(5-2x) , and the LCD would also have been

x^2(5-2x)

but we don't know that, so we have to take the worst-case scenario.

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