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!

Integrate sin (1+ cos ^2 x) ? Please help!

  1. Dec 6, 2008 #1
    First of all, hi I'm new here my name is crisanna. I stumbled upon this site across the web and realised this 's a great site!

    Anyway , here 's my question. Does anyone know how to integrate sin (1 +cos ^2 x) ?

    I tried the method integrate by parts but I got stucked. Below is my attempt :
    u= 1+ cos^2 x

    du/dx = 1/2 x + 1/2 sinxcosx + c ( TBH i dont even know if this part is correct :bugeye: )
    Last edited: Dec 7, 2008
  2. jcsd
  3. Dec 6, 2008 #2
    x's are missing.

    It is not correct. Use the chain rule carefully.
  4. Dec 7, 2008 #3

    Gib Z

    User Avatar
    Homework Helper

    Try a substitution rather than integrating by parts.
  5. Dec 7, 2008 #4
    Tried again and i got du/dx = -2sinxcosx using the chain rule. Was that correct??

    then I was about to use the substitution method..
  6. Dec 24, 2008 #5

    Gib Z

    User Avatar
    Homework Helper

    Hopefully that next substitution was u= cos x. =]
  7. Dec 24, 2008 #6
    Is it
    [tex]\sin \left( 1 + \cos^2 x\right)[/tex]

    [tex]\sin x \cdot \left(1 + \cos^2 x\right)[/tex]

    Quite a difference!
  8. Dec 24, 2008 #7

    [tex] 1 + cos^2x = u [/tex]

    Now you will get a denominator of -sin(2x).

    But we [tex] 1 + cos^2x = u [/tex] hence find x in terms of arccos something. Using the rules of inverse trigo find 2x in terms of arcsin something.

    Now apply parts Twice
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integrate sin (1+ cos ^2 x) ? Please help!
  1. Sin^2 x + cos^2 x = 1 (Replies: 6)