jee-main 2021 Q76

jee-main · India · session4_31aug_shift1 Integration by Substitution Substitution to Transform Integral Form (Show Transformed Expression)

The integral $\int \frac { 1 } { \sqrt [ 4 ] { ( x - 1 ) ^ { 3 } ( x + 2 ) ^ { 5 } } } \mathrm {~d} x$ is equal to : (where $C$ is a constant of integration)
(1) $\frac { 3 } { 4 } \left( \frac { x + 2 } { x - 1 } \right) ^ { \frac { 5 } { 4 } } + C$
(2) $\frac { 4 } { 3 } \left( \frac { x - 1 } { x + 2 } \right) ^ { \frac { 1 } { 4 } } + C$
(3) $\frac { 4 } { 3 } \left( \frac { x - 1 } { x + 2 } \right) ^ { \frac { 5 } { 4 } } + \mathrm { C }$
(4) $\frac { 3 } { 4 } \left( \frac { x + 2 } { x - 1 } \right) ^ { \frac { 1 } { 4 } } + \mathrm { C }$

The integral $\int \frac { 1 } { \sqrt [ 4 ] { ( x - 1 ) ^ { 3 } ( x + 2 ) ^ { 5 } } } \mathrm {~d} x$ is equal to : (where $C$ is a constant of integration)\\
(1) $\frac { 3 } { 4 } \left( \frac { x + 2 } { x - 1 } \right) ^ { \frac { 5 } { 4 } } + C$\\
(2) $\frac { 4 } { 3 } \left( \frac { x - 1 } { x + 2 } \right) ^ { \frac { 1 } { 4 } } + C$\\
(3) $\frac { 4 } { 3 } \left( \frac { x - 1 } { x + 2 } \right) ^ { \frac { 5 } { 4 } } + \mathrm { C }$\\
(4) $\frac { 3 } { 4 } \left( \frac { x + 2 } { x - 1 } \right) ^ { \frac { 1 } { 4 } } + \mathrm { C }$

Paper Questions

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