Integration of tan(x)dx.

\int tan(x)dx

Worldtech Asked on 17th September 2019 in Maths.
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    \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

    techAir Answered on 17th September 2019.
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