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  1. #1
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    integrate 2

    integrate x-1/(x^2-4x+5)
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  2. #2
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    \frac{x-1}{x^2 - 4x + 5} = <br />

    \frac{x - 2 + 1}{x^2 - 4x + 5} =

    \frac{x-2}{x^2 - 4x + 5} + \frac{1}{x^2 - 4x + 4 + 1} =

    \frac{x-2}{x^2 - 4x + 5} + \frac{1}{(x-2)^2 + 1}


    \frac{1}{2} \int \frac{2x-4}{x^2 - 4x + 5} \, dx + \int \frac{1}{(x-2)^2 + 1} \, dx<br />

    \ln{\sqrt{x^2 - 4x + 5}} + \arctan(x-2) + C
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