Substitution Integration

1. May 31, 2009

Physics197

1. The problem statement, all variables and given/known data

∫1/(x^2+2x+2) dx

2. Relevant equations

3. 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

2. May 31, 2009

Pengwuino

Try the substitution u = x+1.

3. Jun 1, 2009

Staff: Mentor

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

Hopefully you know an antiderivative for this integral.