What is the antiderivative of $f(x)=tan (6x)$ ?

Question

3876 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-25T16:39:35

$1/6ln|sec(6x)|$

or if you prefer:

$-1/6ln|cos(6x)|$

The integral of $tan(x)$ is known, and it can be found on most formula sheets with integrals of basic trig functions:

$inttan(x)dx=ln|sec(x)|$

If you want a challenge, try to prove that this is true by using the identity:

$tan(x)=sin(x)/cos(x)$

Then integrate using $u$ -subtitution with $u=cos(x)$ .

What is the antiderivative of f(x)=tan (6x)f(x)=tan (6x)?