- #1

- 12

- 0

## Homework Statement

Evaluate ∫((secx)^2)/[((tanx)^2)+(3tanx)+2]

## Homework Equations

Partial fraction decomposition

## The Attempt at a Solution

So here's what I did:

But this is incorrect. It says the correct answer is -2lnabs([itex]\frac{1}{2tanx+3}[/itex]+[itex]\sqrt{4(tanx+3/2)^{2}-1}[/itex]), which was achieved by making the same u-substitution, completing the square, and then doing a trig substitution. I'm not sure why my method is incorrect. Any help would be great, thanks!