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Math Help - Integral Exercise!

  1. #1
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    Integral Exercise!

    Find the function f where f(x) is f(x)=∫((x-1)^2)/(x^2+1)) f(x)dx - c
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  2. #2
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    Quote Originally Posted by ypatia View Post
    Find the function f where f(x) is f(x)=∫((x-1)^2)/(x^2+1)) f(x)dx - c
    \frac{(x-1)^2}{x^2+1}=\frac{x^2-2x+1}{x^2+1}=\frac{(x^2+1)-2x}{x^2+1}=1-\frac{2x}{x^2+1}

    This is alot better to integrate.

    I hope this helps
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  3. #3
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    Quote Originally Posted by ypatia View Post
    Find the function f where f(x) is f(x)=∫((x-1)^2)/(x^2+1)) f(x)dx - c
    Differentiate both sides of the given equation:

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

    Now re-arrange and integrate: \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.
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