Finding an antiderivative using substitution rule

AI Thread Summary
To find the antiderivative of sec(2x)tan(2x), the substitution u = sec(2x) is effective. This leads to the differential (1/2)du = sec(2x)tan(2x)dx, simplifying the integration process. The method was confirmed to yield the correct answer. The discussion highlights the importance of recognizing the derivative relationship in substitution. Overall, the substitution rule proves useful in solving this integral.
h_k331
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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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<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.
 
replace 2x by u and you have secu 's derivative under the integral sign
 
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
 
Looks good to me!
 
Thank you for the replys.

hk
 
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