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

 

[Benny]

<br /> \sec \left( {2x} \right)\tan \left( {2x} \right) = \frac{{\sin \left( {2x} \right)}}{{\cos ^2 \left( {2x} \right)}}<br />

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 preferred method but it came out to the correct answer.

hk

 

[HallsofIvy]

Looks good to me!

 

[h_k331]

Thank you for the replys.

hk