Partial Fraction Decomposition problem

[sashab]

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($\frac{1}{2tanx+3}$+$\sqrt{4(tanx+3/2)^{2}-1}$), 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!

 

[haruspex]

I agree with your answer (and method!). Seems to me that the other answer is a decreasing function in the range 0 to 1, yet from the integral it should clearly be increasing. If you post all the working of the other method I'll see if I can find the error.

 

[sashab]

Ohh okay, I'm glad it's not incorrect then! Here's the other solution I was referring to :

 

[haruspex]

There's an error here: csc = 1/sec.

 

[sashab]

There's an error here: csc = 1/sec.

Ohh okay I see. Thanks so much for the help! Would you be willing to help me with another partial fraction decomposition question?

 

[haruspex]

Ohh okay I see. Thanks so much for the help! Would you be willing to help me with another partial fraction decomposition question?

Sure, but post it in a new thread for all to see.