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!

Antiderivative help?

  1. Mar 15, 2007 #1

    does anyone know the antiderivative of cotangent or of arcsine? any explanation would be appreciated.
     
  2. jcsd
  3. Mar 15, 2007 #2
    Express cotangent in terms of sines and cosines and then make an appropraite substitution to find its antiderivative, use integration by parts for arcsine.
     
  4. Mar 16, 2007 #3
    You can always try the Integrator. (Making sure, of course, that you triple-check the answer works before doing anything with it!)
     
  5. Mar 16, 2007 #4
  6. Mar 16, 2007 #5

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    I don't see the antiderivative of the arcsine, or cotangent functions on that webpage!
     
  7. Mar 21, 2007 #6
    cot x = d/dx [ln (sin x)]
    arcsin x = d/dx [(1-x²)^½ + x*arcsin x] <--Use integration by parts
     
    Last edited: Mar 21, 2007
  8. Mar 21, 2007 #7

    VietDao29

    User Avatar
    Homework Helper

    [tex]\int \cot x dx = \int \frac{\cos x}{\sin x} dx[/tex]
    Since, the power of cosine function is odd, we can let u = sin x.
    (In fact, the power of sine function is also odd, so letting u = cos x should be fine as well)
    u = sin x ~~~> du = cos x dx
    So, the integral becomes:
    [tex]\int \cot x dx = \int \frac{\cos x}{\sin x} dx = \int \frac{du}{u} = \ln |u| + C = \ln |\sin x| + C[/tex]

    ----------------
    The antiderivative of arcsin can be found by Integration by Parts:
    [tex]\int \arcsin x dx[/tex]
    [tex]u = \arcsin x \Rightarrow du = \frac{dx}{\sqrt{1 - x ^ 2}}[/tex]
    dv = dx ~~~> v = x
    So, your original integral will become:
    [tex]\int \arcsin x dx = x \arcsin x - \int \frac{x dx}{\sqrt{1 - x ^ 2}} = x \arcsin x + \frac{1}{2} \int \frac{d \left( 1 - x ^ 2 \right)}{\sqrt{1 - x ^ 2}} = x \arcsin x + \sqrt{1 - x ^ 2} + C[/tex]
     
  9. Mar 25, 2007 #8
    Thank you

    Thank you for the help everyone I completed the problems. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Antiderivative help?
  1. Antiderivative help (Replies: 13)

  2. Antiderivate arccos (Replies: 2)

Loading...