everyone.
I am having problems to solve this integral:
$$\int\left(\frac1{(x-1)^2*(x+1)^3}\right)dx$$
Any hints will be appreciated
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3Do you know about partial fractions? – Git Gud Jan 07 '14 at 23:09
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Generally, $*$ is multiplication for computer languages, but not for mathematicians. – GEdgar Jan 08 '14 at 01:11
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You can write it as $$ \frac{1}{(x-1)^2 (x+1)^3} = \frac{A}{x-1} + \frac{B}{(x-1)^2} + \frac{C}{x+1} + \frac{D}{(x+1)^2} + \frac{E}{(x+1)^3}$$ where $A,B,C,D,E$ are constants
Added as afterthought
For your reference $$ A=-{{3}\over{16}} , B={{1}\over{8}} , C={{3}\over{16}} , D= {{1}\over{4}} , E={{1}\over{4}} $$
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Thank you. I got another question now. When should i use $A*x+B$ and $A$ in numerator? – dmsmar Jan 07 '14 at 23:17
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@aisas Yes, that will help with the integration too! I find it generally easy to keep the numerators as constants and avoid too many $\log$ identities in the final answer. – user44197 Jan 07 '14 at 23:27