Need help integrating

[kluda06]

⌠(2x-5)/(x²+2x+2) dx

i used u substitution

u=x²+2x+2
du=2x+2dx
du/2x+2=dx

after plugging in dx i ended up getting

-(5/2)⌠1/(x²+2x+2) = -(5/2)Ln |x²+2x+2|

however the answer is ln|x²+2x+2|-7arctan (x+1)+C

What am I doing wrong? please help!

 

[MarkFL]

I would rewrite the integrand as follows:

\(\displaystyle \dfrac{2x-5}{x^2+2x+2}=\dfrac{(2x+2)-7}{x^2+2x+2}=\dfrac{2x+2}{x^2+2x+2}-\dfrac{7}{(x+1)^2+1^2}\)

 

[kluda06]

thank you!