How do you integrate $int (x^2+2x)/(x^2+2x+1)$ using substitution?

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Answer 1 · 2017-02-13T08:04:28

The answer is $=(x+1)+1/(x+1)+C$

Let's factorise,

Therefore,

$int((x^2+2x)dx)/(x^2+2x+1)$

$=int(x(x+2)dx)/(x+1)^2$

Let $u=x+1$

$du=dx$

$x+2=u+1$

$x=u-1$

So,

$int(x(x+2)dx)/(x+1)^2=int((u+1)(u-1)du)/(u^2)$

$=int((u^2-1)du)/u^2$

$=int(1-1/u^2)du$

$=u+1/u$

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

Answer 2 · 2017-02-13T17:08:09

I have found the following results with one substitution:
enter image source here

How do you integrate int (x^2+2x)/(x^2+2x+1)int (x^2+2x)/(x^2+2x+1) using substitution?