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Integration by trig. substitution

  1. May 16, 2005 #1


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    Hello everyone
    I have an exam tomorrow and I would really appreciate if someone could tell me what I did wrong with this exercice. I did it on paper and I scanned it. Here is the link to the scan:

    The answer in the book is sqrt(x^2 + x +5/4) + 2ln(sqrt(x^2 + 2x + 2) + x +1) + C


    It is hosted on imageshack.us
    download it and open it in windows so you can change the zoom size for better viewing

    Thanks a lot in advance !!
  2. jcsd
  3. May 16, 2005 #2
    If u = x + 1, where does u + 1 come from? That is just the first thing I saw, it may lead to your other problems.
  4. May 16, 2005 #3


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    It should be "u+2" in the numerator after doing the first sub.

  5. May 16, 2005 #4


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    Woops. Was this the only problem? I think this only changes the arctg from the final answer and not the ln(..) of the answer. I hate when this type of error happens..
    Last edited: May 16, 2005
  6. May 16, 2005 #5
    When translating from theta back to x, you mistranslated sec(t).

    Next to the triangle you have

    [tex] sec(\theta) = \frac{1}{\cos(\theta)} = \frac{1}{u} [/tex]

    cos(theta) is not u, try looking at it again.
  7. May 16, 2005 #6


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    Thanks a lot :)
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