Math Help - Integral I can't solve

1. 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?

2. Originally Posted by DHS1
$\int\tan(z)(\sec(z))^8dz$

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 $u = \sec{z}$ , $du = (\sec{z}\tan{z}) \, dz$