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Math Help - Integral Question

  1. #1
    Junior Member cinder's Avatar
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    Integral Question

    Need some help..

    \int \frac{\sin(x)}{1+ \cos^2(x)}dx

    Where do I begin? I imagine I need some identities and substitution, but I'm not sure.
    Last edited by cinder; June 26th 2007 at 06:25 PM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cinder View Post
    Need some help..

    \int \frac{sin(x)~dx}{1+ cos^2(x)}
    Substitution.

    Let y = cos(x). Then dy = -sin(x) dx. So your integral becomes:
    \int \frac{sin(x)~dx}{1+ cos^2(x)} = \int \frac{-dy}{1 + y^2}

    Can you do the integral now?

    -Dan
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  3. #3
    Junior Member cinder's Avatar
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    Quote Originally Posted by topsquark View Post
    Substitution.

    Let y = cos(x). Then dy = -sin(x) dx. So your integral becomes:
    \int \frac{sin(x)~dx}{1+ cos^2(x)} = \int \frac{-dy}{1 + y^2}

    Can you do the integral now?

    -Dan
    Okay, I see now. Let me try to integrate it.
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  4. #4
    Junior Member cinder's Avatar
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    Is it -(\arctan(u)+C)?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cinder View Post
    Is it -(\arctan(u)+C)?
    Yup!

    -Dan
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  6. #6
    Junior Member cinder's Avatar
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    Quote Originally Posted by topsquark View Post
    Yup!

    -Dan
    Whoops... I'd throw \cos(x) in place of u though, right?
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cinder View Post
    Whoops... I'd throw \cos(x) in place of u though, right?
    Yup! Yup!

    Actually, if you know the quadrant x is in you can simplify the atn(cos(x)) expression somewhat. But if it's an indefinite integral then you'll have to leave it like that.

    -Dan
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