integral for tan and sec

[kidmo87]

Hello everyone, im trying to solve a problem; sec^6 4x tan4x dx. I was hoping I could get some help with understanding the derivative of u, and how the power is of 2. I circled them in red so no one would get confused. Thanks

 

[pka]

Hello everyone, im trying to solve a problem; sec^6 4x tan4x dx. I was hoping I could get some help with understanding the derivative of u, and how the power is of 2. I circled them in red so no one would get confused. ThanksView attachment 2728

Well I don't blame you there.

I would do this \(\displaystyle \int {{{\sec }^6}(4x)\tan (4x)dx} = \int {{{\sec }^5}(4x)\left[ {\sec (4x)\tan (4x)dx} \right]} = \frac{1}{{24}}{\sec ^6}(4x)\)

 

[kidmo87]

thanks, that does look nicer. How are you getting 1/24 sec^6 (4x)?

 

[pka]

thanks, that does look nicer. How are you getting 1/24 sec^6 (4x)?

\(\displaystyle \int {\dfrac{{{u^5}}}{4}du = \frac{1}{{24}}{u^6}} \)

 

[kidmo87]

ok, I get it. Thanks a lot.