K kluda06 New member Joined Apr 28, 2013 Messages 12 Apr 28, 2013 #1 ⌠(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!
⌠(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 Super Moderator Staff member Joined Nov 24, 2012 Messages 3,021 Apr 28, 2013 #2 I would rewrite the integrand as follows: \(\displaystyle \dfrac{2x-5}{x^2+2x+2}=\dfrac{(2x+2)-7}{x^2+2x+2}=\dfrac{2x+2}{x^2+2x+2}-\dfrac{7}{(x+1)^2+1^2}\)
I would rewrite the integrand as follows: \(\displaystyle \dfrac{2x-5}{x^2+2x+2}=\dfrac{(2x+2)-7}{x^2+2x+2}=\dfrac{2x+2}{x^2+2x+2}-\dfrac{7}{(x+1)^2+1^2}\)
