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}
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}
Show Hint
Even/odd symmetry simplifies many integrals.
Updated On: Jan 9, 2026
- \(x^5\)
- 0
- \(2/3\)
- 2
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
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).
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