- #1
iRaid
- 559
- 8
Homework Statement
[tex]\int \frac{dx}{(x^{2}+2x+2)^{2}}[/tex]
Homework Equations
The Attempt at a Solution
I'm just going to skip down to where something is wrong (the beginning is a u-substitution and trig. substitution so I don't want to type all that out)
After all the trig/u-subs I end up with:
[tex]\int cos^{2}\theta d \theta=\int \frac{1}{2}+\frac{cos2 \theta}{2}d \theta=\frac{\theta}{2}+\frac{sin2\theta}{4}+C[/tex]
So now I substitute back, u=tanθ:
[tex]\frac{tan^{-1}u}{2}+\frac{u}{2\sqrt{u^{2}+1}}[/tex]
and u=x+1:
I THINK THE ERROR IS HERE SOMEWHERE, BUT NOT SURE WHERE
[tex]\frac{1}{2}(tan^{-1}(x+1)+\frac{x+1}{\sqrt{(x+1)^{2}+1}})+C[/tex]Thank you