1. Not finding help here? Sign up for a free 30min 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!

Integration help please

  1. Jul 30, 2007 #1
    Integrating [tex]\frac{1}{(1+sinx)}[/tex]

    i just started learning Integration last week so not exactly sure how to approch this type of question.
  2. jcsd
  3. Jul 30, 2007 #2
    Do you know how to integrate 1/sinx?
  4. Jul 30, 2007 #3
    no this is the first time i have seen where a trigonometric function is on the denominator

    but now that i think about it

    sinx = [tex]\sqrt{1-cos^2x}[/tex]
    and arcsin was equal to [tex]\frac{1}{((1-x^2)}[/tex]

    so i guess i could use the U substituition method
    and then the answer would be...arcsin(cosx)??? im not too sure
    Last edited: Jul 30, 2007
  5. Jul 30, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper

    No, no arcsin. But you might want to try multiplying numerator and denominator by (1-sin(x)). It may look more familiar.
    Last edited: Jul 30, 2007
  6. Jul 30, 2007 #5


    User Avatar
    Gold Member

    You could also try the subsitution u = tan(x/2). It looks a little messy but everything cancels out.
  7. Jul 30, 2007 #6
    well im not sure if im doing the right thing but here goes....

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

    soo then i symplify the equation so that it is


    the i used u = tan[tex](\frac{x}{2})[/tex]

    so i get [tex]\frac{1+u^{2}}{(u+1)^{2}}[/tex]

    What should i do from here or is this the right way at all?
  8. Jul 30, 2007 #7


    User Avatar
    Science Advisor
    Homework Helper

    It looks to me like you are taking the long way around. Try multiplying numerator and denominator of your original problem by (1-sin(x)). You get (1-sinx)/cos^2(x). If you split that into two integrals you shouldn't have any problem with either of them.
  9. Jul 30, 2007 #8


    User Avatar
    Gold Member

    Dick solution is quicker in this case but to integrate things like
    1/(1+cosx+sinx) the substitution u=tan(x/2) is good.
    But notice that it isn't x = tan(u/2) but rather u=tan(x/2). In order to get this into something the the example I gave you can show with so trig identities that if u=tan(x/2) then:
    dx = 2du/(1+u^2)
    sinx = 2u/(1+u^2)
    cosx = (1-u^2)/(1+u^2)
    If you substitue all that you the (1+u^2)s candel out and you get some rational function which you can solve with the typical rational function method (breaking it into elementry functions...)
  10. Jul 30, 2007 #9
    wow by the way i got the answer using what dick said its actually pretty easy once u break it up...now im gonna try Daniels question gonna see if i can get those now :) thnx alot for the help by the way
    the answe was tanx - secx +c
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integration help please