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:

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