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Evaluate: ∫( 5cos^3 x + 3sin^3 x)/(cos^2 x sin^2 x) dx.

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Evaluate: ∫( 5cos3 x + 3sin3 x)/(cos2 x sin2 x) dx.

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1 Answer

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Best answer

We have, 

∫((cosx – sin x)/(cos x + sinx)) (1 + sin2x) dx  

= ∫((cos x – sinx)/( cos x + sinx)) (cos x + sinx)2 dx 

= ∫(cos x – sinx)(cos x + sinx) dx 

 = ∫(cos2 x – sin2 x) dx = ∫cos2x dx 

= (sin 2x/2) + c

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