Please help me evaluate the following integral (click to see) with an appropriate substitution.

Question

babyslapmafro · Answer

$$\int\limits_{}^{}\sec(4x)\tan(4x)$$

babyslapmafro · Answer

would u=tan(4x) be the most simple way to tackle this problem?

anonymous · Answer

well to check you answer you would take the derivatve of the answer the get your original integral. and the derivative of secx is secxtanx

anonymous · Answer

Set u=4x. then du=4dx. 
∫sec(4x)tan(4x) dx = (1/4)∫4*sec(4x)tan(4x) dx = (1/4)∫sec(u)tan(u)du = (1/4)sec(u)= (1/4)sec(4x)
There really isn't any substitution other than the constant due to 4x.

babyslapmafro · Answer

Ok, thank you, I did not know you could use separate substitutions like that...

anonymous · Answer

since it is all multiplication it still has a commutative property like any other function.