1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework: Indefinite Integral

  1. May 3, 2008 #1
    Evaluate the indefinite integral:

    [(e^(4x))/(e^(8x))+9]dx

    -I think that u=e^(2x)
    so then du=e^(2x)dx
    then the answer would end up being [(e^(4x)+9)/(-1)]^(-1)

    but it was incorrect; I think that my u might be wrong and that's where the problem is, but I am not sure. Please help, thank you!
     
  2. jcsd
  3. May 3, 2008 #2
    as in

    [tex]\int (\frac{e^{4x}}{e^{8x}}+9)dx ?[/tex]
    [tex]\int (e^{4x-8x}+9)dx = - \frac{1}{4}e^{-4x}+9x[/tex]

    or as

    [tex]\int (\frac{e^{4x}}{e^{8x}+9})dx ?[/tex]
    [tex]u=e^{8x}+9[/tex]
    [tex]du=8e^{8x}[/tex]
    and then i don't know how to solve this =D
    If that's what you were asking, you got a tough one.
    [still thinking]

    It looks like an integration by parts question, or I am sleepy and can't see the answer D=
    But integration by parts doesn't work in my case still...
     
    Last edited: May 3, 2008
  4. May 3, 2008 #3
    correction on problem

    the second part is the one that we need help on...thank you!!
     
  5. May 3, 2008 #4

    exk

    User Avatar

    [tex]u=e^{4x}[/tex]
    [tex]du=4e^{4x}[/tex]

    [tex]
    \frac{1}{4} \int(\frac{1}{u^{2}+3^{2}})du
    [/tex]

    Can you finish it from there?
     
    Last edited: May 3, 2008
  6. May 3, 2008 #5
    As I was saying.. I must've been smoking something....
     
  7. May 3, 2008 #6
    I always get confused when taking antiderivatives of fractions...how do I go about doing that?
     
  8. May 3, 2008 #7
    natural log?
     
  9. May 3, 2008 #8
    So, I ended up with 1/4lnabs((e^4x)^(2))+9) and got it wrong, what am I doing incorrectly?
     
  10. May 3, 2008 #9

    exk

    User Avatar

    [tex]\int\frac{1}{u^{2}+a^{2}}=\frac{1}{a}tan^{-1}(\frac{u}{a})+C[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Homework: Indefinite Integral
  1. Indefinite Integration (Replies: 11)

  2. Indefinite Integrals (Replies: 4)

  3. Indefinite Integral (Replies: 2)

Loading...