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Thread: Integral I can't solve

  1. May 17th 2009, 05:35 PM #1
    DHS1
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    Integral I can't solve

    \int\tan(z)(\sec(z))^8dz

    I can't figure it out. I know the answer is

    \frac{(\sec(z))^8}{8}

    Can anyone solve this for me?
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  2. May 17th 2009, 05:44 PM #2
    skeeter
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    Quote Originally Posted by DHS1 View Post
    \int\tan(z)(\sec(z))^8dz

    I can't figure it out. I know the answer is

    \frac{(\sec(z))^8}{8}

    Can anyone solve this for me?
    \int \tan{z} \sec^8{z} \, dz = \int \sec^7{z} \, (\sec{z} \, \tan{z}) \, dz

    use elementary substitution ... let u = \sec{z} , du = (\sec{z}\tan{z}) \, dz
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