Question:
The value of \( \int \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx \) is
The value of \( \int \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx \) is
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When dealing with integrals involving trigonometric functions, use substitution and simplify the expression to make integration easier.
Updated On: Dec 11, 2025
- \( \frac{1}{3(1 + \tan^3 x)} + C \)
- \( -\frac{1}{3(1 + \tan^3 x)} + C \)
- \( \frac{1 + \tan^3 x}{3} + C \)
- \( -\frac{3}{1 + \tan^3 x} + C \)
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The Correct Option is B
Solution and Explanation
We use the substitution method to solve this integral. By simplifying the expression using trigonometric identities and performing the integration, we get the solution \( -\frac{1}{3(1 + \tan^3 x)} + C \).
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