What is the Appropriate Substitution for Solving the Integral of x/(x^2+2x+2)dx?

[apiwowar]

integral of x/(x²+2x+2)dx

first thing i did was complete the square to get

x/((x+1)²+1

i tried then having x+1 = tanx but that didnt work out

because of the x on top i can't just set w = x+1

what would the right substitution be?

any hints or help would be appreciated

 

[TheoMcCloskey]

apiwowar - try one more substitution, u = (x+1). This will yield two terms in numerator, thus two fractions, for which you should be able to integrate separately with a little more manipulation.

 

[Cyosis]

Using the substitution $x+1=\tan u$ will work just fine. However the substitution in post #2 will make it easier. Show us where you got stuck.

 

[apiwowar]

i did the substitution that the first guy suggested and got 1/2ln((x+1)²+1) - arctan(x+1)

is that right?

 

[TheoMcCloskey]

That is what I obtained (don't forget constant of integration).