Integration of tan x

Integration of tanx - In this paper, we will discuss how to integrate the following tan (x).

The technique used is the integration of substitution techniques.

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

Notice the integran on the right, we can assume u = cos (x) because the derivatives of cos (x) are -sin (x).

If u = cos (x) then du = -sin (x) dx so we get:

$$\begin{array}{rl}\int tan(x)dx& =\int \frac{sin(x)}{cos(x)}dx\\ & =-\int \frac{du}{u}\\ & =-ln(u)\\ & =-ln(cosx)\end{array}$$

So, $\int tan(x)dx=-ln(cosx)+C$

Note:

$\int \frac{1}{x}dx=ln(x)+C$

ln: natural logarithm.

Hopefully this article, Integration of tanx, useful for readers.