Question

The integral \[ \int\!\frac{\sin^2x\cos^2x}{(\sin^5x+\cos^3x\sin^2x+\sin^3x\cos^2x+x^5+x\cos^5x)}dx \] is of the form}

• A. \(x^5\)
• B. 0
• C. \(2/3\)
• D. 2

Hint:

Even/odd symmetry simplifies many integrals.

Answer 1

The Correct Option is B

The integrand is an odd function overall due to denominator dominant \(x\) and \(x^5\) odd terms, while numerator even. Symmetric limits in debate imply cancellation → value 0. Hence → (B).