How to Integrate 1/(1+2x+x^2) dx Without Getting Stumped

[FUNKER]

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

help

 

[himanshu121]

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

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

Whats the pro

 

[gerben]

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

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

Whats the pro

?
?

 

[gerben]

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

 

[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.