Mathematics

Evaluate: $$\displaystyle\int  \dfrac{ dx} {{{\cos }^2}x{{\left( {1 - \tan x} \right)}^2}} $$


SOLUTION
$$I=\int \dfrac{1}{\cos^{2} x (1- \tan x)^2} dx$$

$$=\int \dfrac{\sec^{2}x}{(1-\tan x)^{2}} dx$$

Let $$\tan x=t \Rightarrow \sec^{2} xdx=dt$$

$$I=\int \dfrac{dt}{(1-t)^{2}}$$

$$I=\dfrac{1}{(1-t)}+C$$

$$I=\dfrac{1}{(1-\tan x)}+C$$
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Subjective Medium Published on 17th 09, 2020
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