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!

Homework Help: How to integrate this !

  1. Nov 4, 2012 #1
    [tex] V = \int \frac{x}{(sin(x^2))^2}.dx [/tex]

    I tried to solve this by parts or by substitution but that doesn't seem to work.
    Any Idea how to solve it :/
  2. jcsd
  3. Nov 4, 2012 #2


    User Avatar
    Science Advisor

    Looks to me like the substitution [itex]u= x^2[/itex] is obvious. With that,
    [tex]\int \frac{x}{sin^2(x^2)}dx= \frac{1}{2}\int \frac{1}{sin^2(u)}du= \frac{1}{2}\int csc^2(x)dx[/tex]
    That's fairly straightforward.
  4. Nov 10, 2012 #3
    ∫x/sin(x²)² dx
    Put x²=t
    ∴ 2x dx=dt
    x dx = dt/2
    Substituting we get,
    1/2∫dt/sin t²
    = 1/2∫cosec²t dt
    = -1/2 cot t + C
    = -1/2 cot²x + C
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook