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$\int \frac{\sin^{2} x \cos^{2} x d x}{{(\sin^{5} x + \cos^{3} x \sin^{2} x + \sin^{3} \cos^{2} x + \cos^{5} x)}^{2}}$

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−11+cos3x+C

131+tan3x+C

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detailed solution

Correct option is B

∫sin2⁡xcos2⁡xdxsin3⁡x+cos3⁡xsin2⁡x+cos2⁡x2=∫sin2⁡xcos2⁡xdxsin3⁡x+cos3⁡x2=∫tan2⁡xsec2⁡xdx1+tan3⁡x2 put t=1+tan3⁡x=13∫dtt2=−13t+C

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∫sin2xcos2x dxsin5x+cos3xsin2x+sin3cos2x+cos5x2

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$\int \frac{\sin^{2} x \cos^{2} x d x}{{(\sin^{5} x + \cos^{3} x \sin^{2} x + \sin^{3} \cos^{2} x + \cos^{5} x)}^{2}}$