Find the integral?

Question

Find the integral of (2 dx)/(x^2-2x) from 3 to infinity.

 

Please show all your work.

Answer 1

Sun,

       The denominator of the integrand can be written as (x-1)²-1 (complete the square) now if you let u=x-1 du=dx and this original integral becomes 

 

-2∫du/(1-u²)=-2tanh^-1(u) +c =-2tanh^-1(x-1)

 

Jim