jee-main 2019 Q84

jee-main · India · session2_08apr_shift2 Integration by Substitution Substitution to Transform Integral Form (Show Transformed Expression)

If $\int \frac { d x } { x ^ { 3 } \left( 1 + x ^ { 6} \right) ^ { \frac { 2 } { 3 } } } = x f ( x ) \left( 1 + x ^ { 6} \right)^{ \frac { 1 } { 3 } } + C$, where $C$ is a constant of integration, then the function $f ( x )$ is equal to
(1) $\frac { 3 } { x ^ { 2 } }$
(2) $- \frac { 1 } { 2 x ^ { 3 } }$
(3) $- \frac { 1 } { 6 x ^ { 3 } }$
(4) $- \frac { 1 } { 2 x ^ { 2 } }$

If $\int \frac { d x } { x ^ { 3 } \left( 1 + x ^ { 6} \right) ^ { \frac { 2 } { 3 } } } = x f ( x ) \left( 1 + x ^ { 6} \right)^{ \frac { 1 } { 3 } } + C$, where $C$ is a constant of integration, then the function $f ( x )$ is equal to\\
(1) $\frac { 3 } { x ^ { 2 } }$\\
(2) $- \frac { 1 } { 2 x ^ { 3 } }$\\
(3) $- \frac { 1 } { 6 x ^ { 3 } }$\\
(4) $- \frac { 1 } { 2 x ^ { 2 } }$

Paper Questions

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