If $\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c$ where c is a constant of integration, then $\lambda f\left( {{\pi \over 3}} \right)$ is equal to

Question

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

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

${9 \over 8}$

-2

$-{9 \over 8}$

Solution

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