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.
#1
h_k331
33
0
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.
replace 2x by u and you have secu 's derivative under the integral sign
#4
h_k331
33
0
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.
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Here is what I tried
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