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

Question

3859 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-25T16:39:35

$\frac{1}{6} ln | sec (6 x) |$ $1/6ln|sec(6x)|$

or if you prefer:

$- \frac{1}{6} ln | cos (6 x) |$ $-1/6ln|cos(6x)|$

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

$\int tan (x) d x = ln | sec (x) |$ $inttan(x)dx=ln|sec(x)|$

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

$tan (x) = \frac{sin (x)}{cos (x)}$ $tan(x)=sin(x)/cos(x)$

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

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