What is the Substitution Method for Integrating a Rational Function?

[Physics197]

Homework Statement

∫1/(x^2+2x+2) dx

Homework Equations

The Attempt at a Solution

u = x^2+2x+2
du = 2dx(x+1)

But I am left with an x and can not find the antiderviative

 

[Pengwuino]

Try the substitution u = x+1.

 

[Mark44]

Using the substitution suggested by Pengwuino, you should get
$$\int \frac{du}{u^2 + 1}$$

Hopefully you know an antiderivative for this integral.