# 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