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!

Calculus : int(cot^3x)dx but why

  1. Nov 28, 2014 #1
    • Member informed about compulsory use of homework template.
    ∫cot^3(x) dx

    = ∫cot^2(x) cot (x) dx

    = ∫(csc^2(x) - 1) cot (x) dx

    = ∫ csc^2(x)) cot (x) dx - ∫cot (x) dx

    = ∫- cot (x) d (cot x) - ln I sin x I

    = - (1/2)cot^2(x) - ln I sin x I + C
    but
    if


    ∫cot^3(x) dx

    = ∫cot^2(x) cot (x) dx

    = ∫(csc^2(x) - 1) cot (x) dx

    = ∫ csc^2(x)) cot (x) dx - ∫cot (x) dx

    = ∫- csc (x) d (csc x) - ln I sin x I

    = - (1/2)csc^2(x) - ln I sin x I + C


    So
    = - (1/2)cot^2(x) + C = = - (1/2)csc^2(x) + C
    csc = cot
    but
    csc^2 = cot^2 +1

    i'm not sure but maybe "1" will add in C ? Please help me
     
  2. jcsd
  3. Nov 28, 2014 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    In general, there is no guarantee that you will get the same integration constant so the 1 can be absorbed into the corresponding constant.

    The check should be to differentiate the result to make sure you get the integrand back.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculus : int(cot^3x)dx but why
  1. Int (1/dx) (Replies: 8)

  2. Int 1/(sin^3x+cos^3x) (Replies: 33)

  3. Integral (x e^-3x dx) (Replies: 2)

  4. Finding ∫x sin^3x dx (Replies: 4)

Loading...