Mathematics

Integrate the following function with respect to $$x$$
$$\dfrac{\cos{x}}{1-\sin{x}}$$


SOLUTION
According to question,
$$\displaystyle \int \dfrac{\cos{x}}{1-\sin{x}}dx$$
Let, $$1-sinx=t$$
$$\Rightarrow$$  $$-cosx.dx=dt$$
$$\Rightarrow$$  $$\displaystyle \int -\dfrac{1}{t}dt$$
$$-lnt+C$$
$$\Rightarrow$$  $$-ln(1-sinx)+C$$
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Subjective Medium Published on 17th 09, 2020
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