Partial Fraction Decomposition problem

  • Thread starter sashab
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  • #1
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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:
tumblr_n3y124QYZc1tsd2vco1_500.jpg


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!
 

Answers and Replies

  • #2
haruspex
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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.
 
  • #3
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Ohh okay, I'm glad it's not incorrect then! Here's the other solution I was referring to :
tumblr_n3y5ulxl4Q1tsd2vco1_1280.png
 
  • #4
haruspex
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There's an error here: csc = 1/sec.
 
  • #5
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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?
 
  • #6
haruspex
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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.
 

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