Integrate: 1/(1+2x+x^2) dx

1. Jul 8, 2004

FUNKER

In an exam i stumbled when i saw this q
integrate:
1/(1+2x+x^2) dx
:grumpy:
help

2. Jul 8, 2004

himanshu121

$$\int \frac{dx}{1+2x+x^2}$$

$$\int \frac{dx}{(1+x)^2}$$

Whats the pro

3. Jul 9, 2004

?????
?????

4. Jul 9, 2004

gerben

$$1 + x^2$$ + $$\frac{1}{3}x^3$$

Last edited: Jul 9, 2004
5. Jul 9, 2004

master_coda

Substitute $u=x+1$. $du=dx$ so we get

$$\int\frac{dx}{(1+x)^2}=\int\frac{du}{u^2}=\int u^{-2}du$$

That should make it a little easier to see what rule you can apply.