appleduardo 2 years ago whats the integral of the following function?

1. appleduardo

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

2. harsh314

take $x ^{2}+2x+1=(x+1)^{2}$ and proceed by substiution

3. harsh314

did u get it..............

4. appleduardo

yeah! but i forgot to type 2 before x^2, :/ so the function is:$\int\limits_{}^{}\frac{ dx }{ 2x^{2} + 2x +1 }$

5. appleduardo

what i did is this: $\frac{ 1 }{ 2 }\int\limits_{}^{}\frac{ dx }{ x ^{2} +2x +1}$ but then i get stuck!

6. harsh314

then divide and multiply the whole denominator by 2$2(x ^{2}+x+\frac{ 1 }{ 2 })$ then you need to make it into a square expression as$x ^{2}+x*2*\frac{ 1 }{ 2 }+\frac{ 1 }{ 4 }-\frac{ 1 }{ 4 }+\frac{ 1 }{ 2 }$add 1/4 and subtract 1/4 then $(x+\frac{ 1 }{ 2 })^{2}=x^{2}+x+\frac{ 1 }{ 4 }$substitute and then solve

7. appleduardo

yeah thanks, i will try and ill post when im done :D

8. appleduardo

i got: $2arc tg \frac{ x +0.5 }{ 0.5 } + c$ is that correct?

9. appleduardo

(correction)$arc tg \frac{ x +0.5 }{ 0.5 } + c$

10. harsh314

the question takes the form................$\frac{ 1 }{ (x+\frac{ 1 }{ 2 })^{2}-(\frac{ 1 }{ \sqrt{2} })^{2} }$