Have i integrated this correctly?

[Dell]

$$\int$$(x-5)/(x²-2x+2)dx

(x-5)/(x²-2x+2)=(x-1-4)/((x-1)²+1)

x-1=t therefore x=t+1

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


$$\int$$(x-5)/(x²-2x+2)dx=$$\int$$(t-4)/(t²+1)dt

=$$\int$$t/(t²+1)dt-4$$\int$$1/(t²+1)dt

=0.5ln|t²+1|-4arctg(t)+c

 

[Mark44]

If you differentiate your answer, you should be able to get back to your original integrand.