Evaluate the integral (x-2)/(x^2-4x+6) dx?

x-2x2-4x6-dx

#1

evaluate the integral (x-2)/(x^2-4x+6) dx?

Answer:

Take the integral:
integral (x-2)/(x^2-4 x+6) dx
For the integrand (x-2)/(x^2-4 x+6), substitute u = x^2-4 x+6 and du = (2 x-4) dx:
= 1/2 integral 1/u du
The integral of 1/u is log(u):
= (log(u))/2+constant
Substitute back for u = x^2-4 x+6:
Answer: = 1/2 log(x^2-4 x+6)+constant