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Need help on integral question

  1. Mar 19, 2007 #1
    Hello, i have a question. This is integral question, but i dont have any program to write the equation with:

    integral (sin5x)^(-2) dx= ?

    Thank you..
     
  2. jcsd
  3. Mar 19, 2007 #2

    cristo

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    This is one of those you should really know, since it can be rewritten cosec2(5x).

    However, if you don't know the antiderivative, then it can be worked out by a few substitutions, the first being u=sin(5x)
     
  4. Mar 19, 2007 #3
    yes i have done using substitution method but can't solve the problem. Can you step by step show me how please? thx
     
  5. Mar 19, 2007 #4

    cristo

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    It's your homework, not mine! Show how you did the first substitution, and we'll go from there.
     
  6. Mar 19, 2007 #5
    ok sorry :smile:
    if i substitute with sin5x,

    integral (sin5x)^(-2) d(sin5x)/5cos5x

    this is how far i can get if i substitute with sin5x as i cant eliminate the cos5x.
    I already tried substituting with cosec5x and sec5x, but still no solution.
     
  7. Mar 19, 2007 #6
    With -d[cot(x)]=(sinx)^(-2) dx ,you can solve it easily.Have a try!
     
  8. Mar 19, 2007 #7

    cristo

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    If you've substituted, why do you still have functions of x in the integral? If you let u=sin(5x), then du=5cos(5x)dx=5[sqrt(1-u2)]. This transforms your integral to [tex]5 \int \frac{du}{u^2\sqrt{1-u^2}}[/tex].

    There you go, I've done one step for you. Now, try the substitution v=1/u.
    If you look back, I said you'll need a few substitutions!


    I did allude to that in my first post.
     
  9. Mar 20, 2007 #8
    ok thx guys i understand now :smile:
     
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