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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

    HallsofIvy

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    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
     
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