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When do you use In or log in Integrals?

  1. Sep 10, 2009 #1
    1.For example

    a.http://img40.imageshack.us/img40/9514/problem2m.png [Broken]

    b.http://img193.imageshack.us/img193/4250/problem2ans.png [Broken]





    When do you use ln in integrals?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 10, 2009 #2

    HallsofIvy

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    One of the things you should have learned early is that
    [tex]\int \frac{1}{x}dx= ln|x|+ C[/tex]

    [itex]\int sin(x) dx[/itex] is, as you first say, - cos(x)+ C. It is certainly NOT equal to "ln|cos(x)|+ C. I don't know why you would even suggest that.
     
  4. Sep 10, 2009 #3
    Sorry ln|cos(x)|+ C+ must be the integral of tan(x) then.
     
  5. Sep 10, 2009 #4

    HallsofIvy

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    Almost. If you let u= cos(x) then du= -sin(x)dx so
    [tex]\int tan(x)dx= \int\frac{sin(x)}{cos(x)}dx= -\int \frac{du}{u}=-ln|u|+ C= -ln|cos(x)|+ C[/tex]
     
  6. Sep 10, 2009 #5

    Mark44

    Staff: Mentor

    BTW, the shorthand form is not In--it is ln, an abbreviation for logarithmus naturalis, Latin for natural logarithm.
     
  7. Sep 10, 2009 #6
    Just find the derivative of ln|cos(x)| and you will be sure, what the correct integral is.

    [-ln|cos(x)| ]'=(-ln(u))'u'=(-1/cos(x))*(-sin(x))=sin(x)/cos(x)=tan(x) :smile:

    So [itex]\int{tan(x)}=-ln|cos(x)|+C[/itex].
     
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