Find the function f where f(x) is f(x)=∫((x-1)^2)/(x^2+1)) f(x)dx - c

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- Mar 14th 2009, 01:18 PMypatiaIntegral Exercise!
Find the function f where f(x) is f(x)=∫((x-1)^2)/(x^2+1)) f(x)dx - c

- Mar 14th 2009, 01:21 PMTheEmptySet
- Mar 29th 2009, 12:52 AMThe Second Solution
Differentiate both sides of the given equation:

$\displaystyle f'(x) = \frac{(x-1)^2}{x^2+1} f(x)$

Now re-arrange and integrate: $\displaystyle \int \frac{f'(x)}{f(x)} \, dx = \int \frac{(x-1)^2}{x^2+1} \, dx$.

The integral on the right hand side is found using the suggestion in the previous reply.