Question

The value of \( \int \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx \) is

• A. \( \frac{1}{3(1 + \tan^3 x)} + C \)
• B. \( -\frac{1}{3(1 + \tan^3 x)} + C \)
• C. \( \frac{1 + \tan^3 x}{3} + C \)
• D. \( -\frac{3}{1 + \tan^3 x} + C \)

Hint:

When dealing with integrals involving trigonometric functions, use substitution and simplify the expression to make integration easier.

Answer 1

The Correct Option is B

We use the substitution method to solve this integral. By simplifying the expression using trigonometric identities and performing the integration, we get the solution \( -\frac{1}{3(1 + \tan^3 x)} + C \).