Integration of tan(x)dx.

\(\int tan(x)dx\)

Worldtech Asked on 17th September 2019 in Maths.
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    \(\int tan(x)dx
    \\\Rightarrow \int tan(x)=\int \left ( \frac{sin(x)}{cos(x)} \right )dx\)

    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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