Finding an antiderivative using substitution rule

1. Jul 19, 2005

h_k331

I'm trying to find the antiderivative of [sec(2x)tan(2x)], I can't figure out what part I should be substituting. Any help is appreciated.

Thanks,
hk

2. Jul 19, 2005

Benny

$$\sec \left( {2x} \right)\tan \left( {2x} \right) = \frac{{\sin \left( {2x} \right)}}{{\cos ^2 \left( {2x} \right)}}$$

You should be able to finish it off.

3. Jul 19, 2005

wisredz

replace 2x by u and you have secu 's derivative under the integral sign

4. Jul 19, 2005

h_k331

I ended up working on it some more and came up with u=sec(2x).
Then (1/2)du=sec(2x)tan(2x)dx. I'm not sure if this is the prefered method but it came out to the correct answer.

hk

5. Jul 19, 2005

HallsofIvy

Staff Emeritus
Looks good to me!

6. Jul 20, 2005