Integral question

Question

let ∫ f(g(x))g'(x) = ∫ (sec2xtan2x)dx.

Identify u=g(x) and du = g'(x)x.

Do not evaluate the integral

Answer 1

 

In case the given statement is

 

     ∫f(g(x))g′(x)dx = ∫sec(2x)tan(2x)dx,

 

     ∫f(g(x))g′(x)dx = ∫f(u)du

 

according to the chain rule where u = g(x).

 

Now,

 

     ∫f(u)du = ∫sec(2x)tan(2x)dx.

 

which holds if

 

     f(u) = (1/2)sin(u)tan(u) and

 

     u = g(x) = 2x.

 

Not sure if these are what the original question is asking for.