Find the integral?

Question

Find the integral (2x-1)/(x-1)^2 dx.

 

Please show all your work. Thanks.

Answer 1

∫(2x-1)/(x-1)² dx

 

Let u = x-1

du = d(x-1) = dx

 

∫(2u+1)/u² du 

 

= ∫2u/u² du + ∫1/u² du

= 2∫u^-1 du + ∫u^-2 du

= 2ln|u| - u^-1 + C

 

= 2ln|x-1| - 1/(x-1) + C