Question

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?

Answer 1

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))

Answer 2

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)).

Answer 3

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