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!

Is this legal ?

  1. Oct 8, 2012 #1
    Is this "legal"?

    [tex]{sinx= \sum^\inf_0 \frac{-1^nx^{2n+1}}{(2n+1)!}}[/tex]

    Now, let's say we take the integral of this: [tex]{\int sinx = \int \sum^\inf_0 \frac{-1^nx^{2n+1}}{(2n+1)!} = \sum^\inf_0 \frac{-1^n}{(2n+1)!} \int x^{2n+1}}[/tex]

    Which we will get: [tex]{\sum^\inf_0 \frac{-1^n}{(2n+1)!} \frac{x^{2n+2}}{2n+2}+C}[/tex]

    Which of course is the power series for cosx (as we expected).

    The reason why I'm asking this is, am I allowed to make this substitution for sinx/lnx?

    I.e: [tex]{\int \frac{sinx}{lnx} = \int \sum^\inf_0 \frac{-1^nx^{2n+1}}{(2n+1)!}*\frac{1}{lnx} = \sum^\inf_0 \frac{-1^n}{(2n+1)!} \int \frac{x^{2n+1}}{lnx} = \sum^\inf_0 \frac{-1^n}{(2n+1)!} Ei((2n+2)lnx)+C}[/tex]

    Thanks for your time and help.

    EDIT: I think mute might've come to this conclusion a while back (I'd have to check my old threads).
     
    Last edited: Oct 8, 2012
  2. jcsd
  3. Oct 8, 2012 #2

    jedishrfu

    Staff: Mentor

    Re: Is this "legal"?

    this is legal math as the integration of x is independent of the summation symbol n.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is this legal ?
Loading...