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Math Help - integrate (secx)^4

  1. #1
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    integrate (secx)^4

    integrate (secx)^4

    Please help,

    Thanks
    Bryn
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Bryn View Post
    integrate (secx)^4

    Please help,

    Thanks
    Bryn
    \int \sec^4x \, dx = \int (\sec^2x)\sec^2x \, dx = \int (1 + \tan^2x)\sec^2x \, dx

    set u = \tan x...
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  3. #3
    Eater of Worlds
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    If you want the easy way out, use the general formula:

    \int{sec^{n}(u)}du=\frac{1}{n-1}sec^{n-2}(u)tan(u)+\frac{n-2}{n-1}\int{sec^{n-2}(u)}du

    or proceed:

    \int{sec^{4}(x)}dx=\int(1+tan^{2}(x))sec^{2}(x)dx

    =\int(sec^{2}(x)+tan^{2}(x)sec^{2}(x))dx

    =\int{tan^{2}(x)}dx+\int{tan^{2}(x)sec^{2}(x)}dx

    The second half let u=tan(x), \;\ du=sec^{2}(x)dx
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