1. Limited time only! Sign up for a free 30min personal 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 Help: Integration how to start

  1. Apr 20, 2005 #1
    what is the integral of [tex]ln(1+2^x)[/tex]

    [tex]\int ln(1+2^x)=\frac{2^xln(2)}{1+2^x} [/tex]

    is this correct?
  2. jcsd
  3. Apr 20, 2005 #2
    Differentiate and see what you get.
  4. Apr 20, 2005 #3

    [tex] u = 2^x+1, du = 2^xln(2) [/tex]


    [tex] \int ln(1+2^x) dx = ln(2)\int (u-1)ln(u) du [/tex]

    Which can be done by parts.
  5. Apr 20, 2005 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    That result you got looks suspiciously like the derivative of [itex] \ln(1+2^x) [/itex]! What I'm saying is, it looks like you differentiated using the chain rule:

    let u = 1 + 2^x

    [tex] \frac{d}{dx}[\ln(1+2^x)] = \frac{d}{dx}(\ln u) [/tex]

    [tex] = \frac{1}{u} \frac{du}{dx} [/tex]

    [tex] = \left(\frac{1}{1+2^x}\right) \frac{d}{dx}(1+2^x) [/tex]

    [tex] = \frac{(\ln2)2^x}{1+2^x} [/tex]

    But you were supposed to integrate! :smile:

    I just thought I'd point that out, so you could see the mistake.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook