# Homework Help: Have i integrated this correctly?

1. Jan 26, 2009

### 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

2. Jan 26, 2009

### Staff: Mentor

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