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’
\(\\=-ln\left | cos(x) \right |+C\)