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Integration. Where is the mistake? (if there is)

  1. Apr 16, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-4-17_1-2-37.png

    2. Relevant equations


    3. The attempt at a solution
    My Solution:
    upload_2017-4-17_1-2-59.png

    My Friend Solution:
    upload_2017-4-17_1-3-22.png


    Are we both right?
    If not, who is right? and what is the mistake in other's solution!

    Thanks!!
     
  2. jcsd
  3. Apr 16, 2017 #2
    You are correct. The problem with your friend's solution is the integration itself, what is the integral of tan(x)sec2(x)?
     
  4. Apr 16, 2017 #3

    vela

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    Both answers are correct.
     
  5. Apr 16, 2017 #4

    Mark44

    Staff: Mentor

    Your solution is correct, and your friend's solution is almost correct. Your friend wrote ##\frac{\tan x^2} 2 + C##, but possibly meant to write ##\frac{\tan^2(x)} 2 + C##. Although this is different from what you found, the corrected answer from your friend differs only by a constant from your answer. Note that ##\sec^2(x) = \tan^2(x) + 1##, so ##\frac{\sec^2(x)}{2} = \frac{\tan^2(x)}{2} + \frac 1 2##
     
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