Mathematics

Integrate: $$f(x)=\dfrac { \sin ^{ 3 }{ x } +\cos ^{ 3 }{ x }  }{ \sin ^{ 2 }{ x } \cos ^{ 2 }{ x }  }$$ 


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

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

$$ = \int \sec x \tan x dx + \int \csc x \cot x dx$$

$$ = \sec x - \csc x + c$$ (Ans)
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Subjective Medium Published on 17th 09, 2020
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