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Thread: Trig Simplification

  1. #1
    Member WhoCares357's Avatar
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    Trig Simplification

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

    How did wolframalpha simplify it? Or did I just simplify it incorrectly?
    Last edited by mr fantastic; Oct 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:
    $\displaystyle \int \frac{dx}{x^4\sqrt{x^2+3}}$
    - Wolfram|Alpha
    I don't understand how the software came up with $\displaystyle \frac {1}{9}cot^3(u)*csc(u)$
    When I simplified it the same way it did I came up with
    $\displaystyle \frac{sec(u)}{9tan^4(u)}$

    How did wolframalpha simplify it? Or did I just simplify it incorrectly?
    The two expressions are equivalent. Substitute $\displaystyle \tan u = \frac{\sin u}{\cos u}$, $\displaystyle \cot u = \frac{\cos u}{\sin u}$ 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 $\displaystyle \tan u = \frac{\sin u}{\cos u}$, $\displaystyle \cot u = \frac{\cos u}{\sin u}$ etc. to see this.
    Thanks.
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