Mathematics

$$\displaystyle \int\dfrac {\cos 2x+2\sin^{2}x}{\cos^{2}x}dx$$


SOLUTION

Consider the following question.

$$ I=\int_{{}}^{{}}{\dfrac{\cos 2x+2{{\sin }^{2}}x}{{{\cos }^{2}}x}}dx $$

$$ =\int_{{}}^{{}}{\dfrac{{{\cos }^{2}}x-{{\sin }^{2}}x+2{{\sin }^{2}}x}{{{\cos }^{2}}x}}dx $$

$$ =\int_{{}}^{{}}{\dfrac{{{\sin }^{2}}x+{{\cos }^{2}}x}{{{\cos }^{2}}x}}dx $$

$$ =\int_{{}}^{{}}{{{\sec }^{2}}xdx} $$

$$ =\tan x+C $$


Hence, this is the required answer.

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Subjective Medium Published on 17th 09, 2020
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