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: Find this integration

  1. Oct 6, 2013 #1

    utkarshakash

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    [itex]\displaystyle \int_0^1 \dfrac{xe^{tan^{-1}x}}{\sqrt{1+x^2}} dx [/itex]

    2. Relevant equations

    3. The attempt at a solution
    Let tan^-1 (x) = t
    x = tant
    dt=dx/sqrt{1+x^2}
    The integral then reduces to

    [itex]\displaystyle \int_0^{\pi/4} tante^tdt [/itex]

    Applying integration by parts by taking tant as 1st function

    [itex]tant e^t - \displaystyle \int sec^2te^t dt [/itex]

    This has made the problem more complicated instead of simplifying.
     
  2. jcsd
  3. Oct 6, 2013 #2
    $$\frac{d}{dx}\left(\arctan(x)\right) ≠ \frac{1}{\sqrt{1+x^2}}$$
    To use the substitution, multiply and divide by ##\sqrt{1+x^2}##.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted