# Complicated Integral

• February 20th 2010, 07:24 AM
Keithfert488
Complicated Integral
$\int -\cos({\cos({\tan (x)})})\cdot \sin{\tan(x)}\cdot \sec ^2(x)dx$

I have absolutely no clue how to start.
• February 20th 2010, 07:44 AM
skeeter
Quote:

Originally Posted by Keithfert488
$\int -\cos({\cos({\tan (x)})})\cdot \sin{\tan(x)}\cdot \sec ^2(x)dx$

I have absolutely no clue how to start.

$u = \cos(\tan{x})$

$du = -\sin(\tan{x}) \cdot \sec^2{x} \, dx
$

substitute ...
• February 20th 2010, 07:48 AM
Keithfert488
Wow that's a lot simpler than it looks.

So its just

$\sin({\cos({\tan({x})})})$?
• February 20th 2010, 08:29 AM
skeeter
Quote:

Originally Posted by Keithfert488
Wow that's a lot simpler than it looks.

So its just

$\sin({\cos({\tan({x})})})$?

check it ...

$\frac{d}{dx} \sin[\cos(\tan{x})] = ?$