Need help on integral question

  • Thread starter Mag|cK
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  • #1
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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..
 

Answers and Replies

  • #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)
 
  • #3
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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)
yes i have done using substitution method but can't solve the problem. Can you step by step show me how please? thx
 
  • #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.
 
  • #5
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It's your homework, not mine! Show how you did the first substitution, and we'll go from there.
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.
 
  • #6
jakcn001
With -d[cot(x)]=(sinx)^(-2) dx ,you can solve it easily.Have a try!
 
  • #7
cristo
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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.
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.
I already tried substituting with cosec5x and sec5x, but still no solution.
If you look back, I said you'll need a few substitutions!


With -d[cot(x)]=(sinx)^(-2) dx ,you can solve it easily.Have a try!
I did allude to that in my first post.
 
  • #8
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ok thx guys i understand now :smile:
 

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