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Math Help - Trig Simplification

  1. #1
    Member WhoCares357's Avatar
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    Trig Simplification

    Originally I had this integrand:
    \int \frac{dx}{x^4\sqrt{x^2+3}}
    http://www.wolframalpha.com/input/?i...8x^2%2B3%29%29
    I don't understand how the software came up with \frac {1}{9}cot^3(u)*csc(u)
    When I simplified it the same way it did I came up with
    \frac{sec(u)}{9tan^4(u)}

    How did wolframalpha simplify it? Or did I just simplify it incorrectly?
    Last edited by mr fantastic; October 20th 2009 at 04:59 PM. Reason: Added url tags
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by WhoCares357 View Post
    Originally I had this integrand:
    \int \frac{dx}{x^4\sqrt{x^2+3}}
    - Wolfram|Alpha
    I don't understand how the software came up with \frac {1}{9}cot^3(u)*csc(u)
    When I simplified it the same way it did I came up with
    \frac{sec(u)}{9tan^4(u)}

    How did wolframalpha simplify it? Or did I just simplify it incorrectly?
    The two expressions are equivalent. Substitute \tan u = \frac{\sin u}{\cos u}, \cot u = \frac{\cos u}{\sin u} etc. to see this.
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  3. #3
    Member WhoCares357's Avatar
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    Quote Originally Posted by mr fantastic View Post
    The two expressions are equivalent. Substitute \tan u = \frac{\sin u}{\cos u}, \cot u = \frac{\cos u}{\sin u} etc. to see this.
    Thanks.
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