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Solve this following

Question:

If $\int \frac{\cos x d x}{\sin ^{3} x\left(1+\sin ^{6} x\right)^{2 / 3}}=f(x)\left(1+\sin ^{6} x\right)^{1 / \lambda}+c$

where $\mathrm{c}$ is a constant of integration, then $\lambda f\left(\frac{\pi}{3}\right)$ is equal to

  1. $-2$

  2. $-\frac{9}{8}$

  3. 2

  4. $\frac{9}{8}$


Correct Option: 1

Solution:

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