# Finding an antiderivative using substitution rule

#### 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

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#### 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.

#### wisredz

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

#### 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

#### HallsofIvy

Homework Helper
Looks good to me!

hk

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