integration by substitution: int [ sec(4x) tan(4x) ] dx

[xc630]

Hello I owuld appreicate some hlep with this integral

the integral of sec 4x tan 4x dx

I am not sure what to let u=
if Ilet it = sec 4x tan 4x then du = sec 4x dx

But then that would not work out. Am i allowed to put cos 4x outside th eintegral so the sec 4x cancels?

 

[galactus]

I'm an idiot. I posted the wrong integral before.

\(\displaystyle \L\\\int{tan(4x)sec(4x)}dx\)

Let \(\displaystyle \L\\u=sec(4x) \;\ and \;\ du=4sec(4x)tan(4x)dx \;\ and \;\ \frac{du}{4}=sec(4x)tan(4x)dx\)

Then you simply have:

\(\displaystyle \L\\\frac{1}{4}\int{du}\)

 

[xc630]

Sorru i typed the integral in a confusing fashion.It is the integral of sex (4x) tan (4x) dx. No exponents

 

[galactus]

Yes, I realize that. I fix.