Hi
Is this 'supposed' to be solved with partial fractions decomposition?
Problem:
Find all primitive functions to:
$\displaystyle \int \frac{1}{x^{2}(x-1)^{3}} \; dx $
Kinda need some starting help if so is the case, thx!
Hi
im sorry but it is $\displaystyle \frac{1}{x^{2}\cdot (x-1)^{3}} $ and not $\displaystyle \frac{1}{x^{3}\cdot (x-1)^{3}} $
But, should I do:
$\displaystyle \frac{1}{x^{2}\cdot (x-1)^{3}} = \frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{(x-1)}+\frac{D}{(x-1)^{2}} + \frac{E}{(x-1)^{3}} $ ?
That's a bit .... final!
There are several ways of doing it. None are 'right' or 'wrong'. Partial fractions is one way. And there's no doubt about the usefulness and ease of the reciprocal substitution, which is another way.
However, I suspect that whoever set this question would have had partial fractions in mind.