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- anonymous

I need to find the integral of tan(2x). The answer I am getting is (1/2)ln|sec(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

- katieb

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- anonymous

Ok. 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

the 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

Thank you for the help guys. Apparently -log(cos(u)) = -ln|sec(u)|

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