What is the integral of $int tan(2x) dx$ ?

Question

29519 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-19T15:23:47

$inttan(2x)dx =-1/2ln|cos(2x)|+C$

We will proceed using substitution, along with the fact that $int1/xdx = ln|x|+C$

Let $u = cos(2x) => du = -2sin(2x)dx$

Then we have

$inttan(2x)dx = intsin(2x)/cos(2x)dx$

$=-1/2int1/cos(2x)(-2sin(2x))dx$

$=-1/2int1/udu$

$=-1/2ln|u|+C$

$=-1/2ln|cos(2x)|+C$

What is the integral of int tan(2x) dxint tan(2x) dx?