Mathematics

Solve:
$$\displaystyle \int \dfrac { \sin ^ { 3 } x + \cos ^ { 3 } x } { \sin ^ { 2 } x \cos ^ { 2 } x } d x$$


SOLUTION
$$ \int \dfrac{(sin^{3}+cos^{3}x)}{sin^{2}x\cos^{2}x}dx $$

$$ = \int (\dfrac{sin x}{\cos^{2}x}+\dfrac{\cos x}{\sin^{2}x})dx = \int (\sec x\tan x+cosec\,xcotx)dx $$

$$ = sec x-cosec x+c $$

$$ = \dfrac{1}{\cos x}-\dfrac{1}{\sin x}+c $$

$$ = \dfrac{\sin x-\cos x}{\sin x\,\cos x}+c $$
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Subjective Medium Published on 17th 09, 2020
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