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U substitution and integration by parts

  1. May 23, 2012 #1
    I would think because of this

    Screenshot2012-05-23at73955PM.png

    The following problem:

    Screenshot2012-05-23at72700PM.png

    At this stage they should use integration by parts:

    Screenshot2012-05-23at74154PM.png

    However, maybe integration by parts is only useful when one of the parts is e^x ln or a trigonometric formula.
     
    Last edited: May 23, 2012
  2. jcsd
  3. May 23, 2012 #2
    Integration by parts can be useful whenever the integrand is a product of two functions. But it is not always the easiest method to use. For instance, the integral [itex]\int(u-1)\sqrt{u}du=\int(u^{3/2}-u^{1/2})du[/itex] can easily be solved using the power rule in reverse. Of course, you could solve it using integration by parts as well, but it's just more work than is necessary.
     
  4. May 23, 2012 #3
    good, thanks.
     
  5. May 23, 2012 #4
    What would be your u and what would be your dv?

    Using integration by parts might work, but I feel that even if it does work it will be much more work than using u substitution.


    Is the problem here that you don't find the u substitution they used to be 'legal'?
     
  6. May 23, 2012 #5
    Yea, it doesn't seem legal, because I thought you couldn't take the product of two functions in an integrand.
     
  7. May 23, 2012 #6

    jgens

    User Avatar
    Gold Member

    You need to work on being more precise. The integrand of [itex]\int_0^1 x^2 \mathrm{d}x[/itex] is the product of two functions but is clearly integrable.
     
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