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Math Help - Integral I can't solve

  1. #1
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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. #2
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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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