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: Trigonometric substitution

  1. Oct 16, 2008 #1
  2. jcsd
  3. Oct 16, 2008 #2
    I should probably mention that the answer is supposed to be:

    2*arctan(2x)+4x/(4x^2+1) +C
     
  4. Oct 16, 2008 #3

    HallsofIvy

    User Avatar
    Science Advisor

    I didn't go through that in detail but it looks like a very strange way to attack the problem! You have a square of a square and you write it as a fourth power of a square root of a square so you can apply a trig substitution!
    You don't need the square root to apply a trig substitution. Let 2x= tan t and 4x2+ 1= tan2 t+ 1= sec2. (4x2+ 1)2= sec4 t and 2dx= sec2 t dt. Your integral becomes
    [tex]\int\frac{8dx}{(4x^2+ 1)^2}= \int \frac{4dt}{sec^2 t}= 4\int cos^2 t dt[/itex]
    That should be easy.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook