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Can someone confirm this U sub is legal?

  1. Sep 12, 2007 #1
    [tex]\int e^{-4x} dx\\ = \int e^x *e^{-3x}[/tex] let u=e^x so du=e^x dx

    so [tex]\int u^{-3} du[/tex]

    =[tex] -\frac{1}{2}e^{-2x}+c[/tex]

    Thanks,
    Casey
     
  2. jcsd
  3. Sep 12, 2007 #2
    You made a mistake in the first line, however, it is easy to fix the resulting steps. It should be [itex]e^x \times e^{-5x}[/itex]. I think your method works, however, I think the substitution [itex]u = -4x[/itex] is much easier.

    Also, remember that you can check to see if your answer is correct by taking the derivative at the end.
     
  4. Sep 12, 2007 #3
    [tex]\int e^{-4x} dx\\ = \int e^{-x} *e^{-3x}[/tex]

    you forgot the negative sign on [tex]e^x[/tex].

    But as mattmns above me suggested, just use u = -4x
     
  5. Sep 12, 2007 #4
    Oh yeah..it's not a power to a power.

    I did it both ways, and yes they are equal,...and u=-4x is easier.

    [tex] -\frac{1}{4}e^{-4x}[/tex]

    Thanks,
    Casey
     
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