calculus

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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 -

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 -

Sorry I typed out the wrong answer. Why would I have 3 fractions though? Because it's x^2?

• calculus -

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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