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Evaluate the integral of (x+2) / (x2 – 4x + 4)

Compute the following integral.

    \[ \int \frac{x+2}{x^2 - 4x + 4} \, dx. \]


We can compute this integral by some rearranging,

    \begin{align*}  \int \frac{x+2}{x^2 - 4x + 4} \, dx &= \int \frac{x-2}{x^2 - 4x + 4} \, dx + 4 \int \frac{1}{x^2 - 4x + 4} \, dx \\[10pt]  &= \int \frac{x-2}{(x-2)^2} \, dx + 4 \int \frac{1}{(x-2)^2} \, dx \\[10pt]  &= \log |x-2| - \frac{4}{x-2} + C. \end{align*}

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