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anonymous
 5 years ago
I need to find the integral of tan(2x). The answer I am getting is (1/2)lnsec(2x)+C.
However, this isn't one of the answer choices. I may have perhaps done it wrong is there any other way to do this and arrive at a different answer or are the answer choices wrong?
anonymous
 5 years ago
I need to find the integral of tan(2x). The answer I am getting is (1/2)lnsec(2x)+C. However, this isn't one of the answer choices. I may have perhaps done it wrong is there any other way to do this and arrive at a different answer or are the answer choices wrong?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok. So let's use the method of substitution. In this case you get ... \[\int\limits_{?}^{?} \tan(2x)dx\] from here we will substitute. So let u = 2x. Hence du/dx = 1/2. So now plug this back into the formula and you will get \[\int\limits_{?}^{?} (1/2)tan(u)du\] You know that the integral of tan(u) = log(cos(u)). Hence, substituting in the u=2x will result in the answer 0.5log(cos(2x))

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the table of integrals should be at the back of your calculus book, it's pretty helpful. then you dont have to derive how the integral of tan(u) = log(cos(u)).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you for the help guys. Apparently log(cos(u)) = lnsec(u)
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