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Partial Fraction Decomposition

  1. Apr 12, 2014 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    Partial fraction decomposition

    3. 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!
     
  2. jcsd
  3. Apr 12, 2014 #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.
     
  4. Apr 12, 2014 #3
    Ohh okay, I'm glad it's not incorrect then! Here's the other solution I was referring to : tumblr_n3y5ulxl4Q1tsd2vco1_1280.png
     
  5. Apr 12, 2014 #4

    haruspex

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    There's an error here: csc = 1/sec.
     
  6. Apr 12, 2014 #5
    Ohh okay I see. Thanks so much for the help! Would you be willing to help me with another partial fraction decomposition question?
     
  7. Apr 13, 2014 #6

    haruspex

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