[tex]\int[/tex](x-5)/(x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}-2x+2)dx

(x-5)/(x^{2}-2x+2)=(x-1-4)/((x-1)^{2}+1)

x-1=t therefore x=t+1

dx=x'dt=(t+1)'dt=dt

[tex]\int[/tex](x-5)/(x^{2}-2x+2)dx=[tex]\int[/tex](t-4)/(t^{2}+1)dt

=[tex]\int[/tex]t/(t^{2}+1)dt-4[tex]\int[/tex]1/(t^{2}+1)dt

=0.5ln|t^{2}+1|-4arctg(t)+c

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# Homework Help: Have i integrated this correctly?

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