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Math Help - [SOLVED] integral

  1. #1
    Member i_zz_y_ill's Avatar
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    [SOLVED] integral

    I have completely lost some sort of technique for this integral, could somebody help. thanks
    \int\frac{sin(x)}{cos^2(x)}dx I know the answer is sec^2(x)but I don't know how it was got?
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  2. #2
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    Quote Originally Posted by i_zz_y_ill View Post
    I have completely lost some sort of technique for this integral, could somebody help. thanks
    \int\frac{sin(x)}{cos^2(x)}dx I know the answer is sec^2(x)but I don't know how it was got?
    \frac{\sin{x}}{\cos^2{x}} = \frac{1}{\cos{x}} \cdot \frac{\sin{x}}{\cos{x}} = \sec{x} \cdot \tan{x}

    \int \sec{x} \cdot \tan{x} \, dx = \sec{x} + C
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  3. #3
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    -u=Cosx,\ du=Sinxdx

    \int{\frac{du}{u^2}}=\int{u^{-2}du}=-u^{-1}+C=Secx+C
    Last edited by Archie Meade; January 15th 2010 at 05:28 PM. Reason: typo
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  4. #4
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    Quote Originally Posted by Archie Meade View Post
    u=Cosx,\ du=\textcolor{red}{-}Sinxdx

    \int\textcolor{red}{-}{\frac{du}{u^2}}=\int{\textcolor{red}{-}u^{-2}du}=u^{-1}+C=Secx+C
    ...
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  5. #5
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    nice one, Skeeter!
    my brain always seems to shut down at this time of night!
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