The integral ^ 2 x ^ 2 x ( ^ 3 x+ ^ 3 x )^ 2 d x equal to:
Mathematics · JEE Main · NTA Exams — Integral Calculus
The integral \[\int \frac{\sin ^{2} x \cos ^{2} x}{\left(\sin ^{3} x+\cos ^{3} x\right)^{2}} d x\] equal to:
- \(\frac{1}{\left(1+\cot ^{3} x\right)}+c\)
- \(-\frac{1}{3\left(1+\tan ^{3} x\right)}+c\)
- \[\frac{\sin ^{3} x}{\left(1+\cos ^{3} x\right)}+c\]
- \[-\frac{\cos ^{3} x}{3\left(1+\sin ^{3} x\right)}+c\]
Answer
(B) - 1 3 (1+ ^ 3 x ) +c
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