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Homework Help: Find the indefinite integral by u-sub

  1. Apr 20, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    [itex]u=1+\sqrt{2x} \Rightarrow \sqrt{2x}=u-1[/itex]
    [itex]du=1/\sqrt{2x}dx \Rightarrow \sqrt{2x}du=dx[/itex]

    3. The attempt at a solution

    [itex]\int1/(1+\sqrt{2x})\,dx = \int\sqrt{2x}/(1+\sqrt{2x})\,du = \int(u-1)/u\,du = \int\,du-\int1/u\,du = u-ln|u|+C = 1+\sqrt{2x}-ln|1+\sqrt{2x}|+C[/itex]

    The book im using has the answer as:

    Where am i going wrong?
    Last edited: Apr 20, 2013
  2. jcsd
  3. Apr 20, 2013 #2


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    Homework Helper

    That "extra" 1 in your answer can be "absorbed" into the arbitrary constant C (so you can drop the 1). The answers are equivalent.
  4. Apr 20, 2013 #3
    Oh ok. Thank you curious.
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