Integration by using trig. substitution

[ridgej]

Hi, I am completely stuck and have been working around this problem for about an hour or so.
I have to show work in solving an integral using trig. substitution, and possibly other techniques like partial fraction decomposition.

The problem is this:
Evaluate the following integral by using trig. substitution. Show all your work and answers clearly and in detail. All integrals must be evaluated without a calculator or a table of integrals.

Int(dx/(x^2 + 2x + 2)), with respect to x.

I hope you can help me!

 

[stapel]

Where are you stuck? You completed the square in the denominator, converting it to the form (x + a)[sup:1z957b03]2[/sup:1z957b03] + b[sup:1z957b03]2[/sup:1z957b03], picked the inverse-trig derivative of the form 1/(1 + x[sup:1z957b03]2[/sup:1z957b03]), did some u-substitution, and... then what?

Please be complete. Thank you!

Eliz.