# Integration of tan(x)dx.

\(\int tan(x)dx

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

\\\Rightarrow \int tan(x)=\int \left ( \frac{sin(x)}{cos(x)} \right )dx\)

Let t=cos(x)

\(\\\Rightarrow\frac{dt}{dx} =\frac{d}{dx}cos(x)=-sin(x)

\\\Rightarrow dx=-sin(x)dt

\\= -\int \frac{1}{t}dt

\\=-ln\left | t \right |+C\)

On putting the value of ‘t’

\(\\=-ln\left | cos(x) \right |+C\)