# Math Help - integrate (secx)^4

1. ## integrate (secx)^4

integrate (secx)^4

Thanks
Bryn

2. Originally Posted by Bryn
integrate (secx)^4

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

set $u = \tan x$...

3. 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 $u=tan(x), \;\ du=sec^{2}(x)dx$