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Math Help - Integral x/x^2-2x+3

  1. #1
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    Integral x/x^2-2x+3

    \int \frac {x}{x^2-2x+3}dx

    The model answer is \frac {ln(x^2-2x+3)}{2}+\frac{artan\frac{x+1}{\sqrt{2}}}{\sqrt{2  }}+C

    First step, do I make u=x^2-2x+3?
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  2. #2
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    Quote Originally Posted by cammywhite View Post
    \int \frac {x}{x^2-2x+3}dx

    The model answer is \frac {ln(x^2-2x+3)}{2}+\frac{artan\frac{x+1}{\sqrt{2}}}{\sqrt{2  }}+C

    First step, do I make u=x^2-2x+3?

    First start by completing the square in the denominator

    \int \frac {x}{(x-1)^2+2}dx Now let u=x-1 \implies du=dx

    \int \frac{u+1}{u^2+2}du=\int \frac{u}{u^2+2}du+\int \frac{1}{u^2+2}du

    You should be able to finish from here
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