Question #1377f

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Answer 1 · 2017-04-16T23:49:58

#2x-1/(x-1)+C#

#int(2x^2-4x+3)/(x-1)^2dx#

Let #u=x-1#. This implies that #x=u+1# and #du=dx#. Then:

#=int(2(u+1)^2-4(u+1)+3)/u^2du#

Expanding and combining like terms:

#=int(2u^2+1)/u^2du#

#=int(2+1/u^2)du#

#=2u-1/u+C#

#=2(x-1)-1/(x-1)+C#

Expanding #2(x-1)#, we see that the #-2# combines with the constant of integration:

#=2x-1/(x-1)+C#