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!

Primitive function

  1. Jun 7, 2005 #1
    I don't know how to find this primitive function:

    \int \frac{dx}{(1+\tan x)(1+\tan^2 x)}

    I tried substitutions [itex]t = \tan x[/itex] or [itex]t = 1 + \tan x[/itex], but it didn't seem to help me lot...

    Could someone please point me to the right direction?

    Thank you.
  2. jcsd
  3. Jun 7, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    1. Set [tex]t=tan(x)\to\frac{dt}{dx}=\frac{1}{\cos^{2}(x)}=tan^{2}x+1\to{dx}=\frac{dt}{t^{2}+1}[/tex]
    Thus, you've got:
    This can be solved by partial fractions decomposition.
  4. Jun 7, 2005 #3
    Thank you arildno, I made a mistake that I didn't simply change tan x = t and dx = dt/t^2 + 1, instead I expressed tan x as sin x / cos x and divided the denominator with cos^2 x and it turned into crazy powers of t. Your method works great, thanks.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Primitive function
  1. Primitive roots (Replies: 1)

  2. Primitive roots? (Replies: 7)

  3. Length of primitive cell (Replies: 24)