JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

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

where

c

is a constant of integration, then is equal to

View answer and explanation

Correct option: C

-2

Option C (-2) is correct because by substituting

t = \frac{1}{{{\sin }^6}x} + 1 = {t^3}

and solving the integral, we can find the value of

\lambda f(\frac{\pi}{3})

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