Integral of tan³(x) using the identity tan²(x)+1=sec²(x)

[november1992]

Homework Statement

∫$tan^{3}$x dx

Homework Equations

$tan^{2}x$+1 = $sec^{2}$x

$tan^{3}$x = $tan^{2}$x * tan(x)

The Attempt at a Solution

∫$tan^{2}$x * tan(x) dx

∫($sec^{2}$x -1 ) tan(x) dx

∫($sec^{2}$xtan(x) -∫tan(x)

∫u du - $sec^{2}$x

$u^{2}$/2 - $sec^{2}$x

$tan^{2}$x/2 - $sec^{2}$x

 

[november1992]

Oh damn. I just realized integral of tanx is ln|secx|.

I got it wrong on my test :(