Consider the equation $$\int _ { 1 } ^ { e } \frac { \left( \log _ { \mathrm { e } } x \right) ^ { 1 / 2 } } { x \left( a - \left( \log _ { \mathrm { e } } x \right) ^ { 3 / 2 } \right) ^ { 2 } } d x = 1 , \quad a \in ( - \infty , 0 ) \cup ( 1 , \infty )$$ Which of the following statements is/are TRUE ? (A) No $a$ satisfies the above equation (B) An integer $a$ satisfies the above equation (C) An irrational number $a$ satisfies the above equation (D) More than one $a$ satisfy the above equation
Consider the equation
$$\int _ { 1 } ^ { e } \frac { \left( \log _ { \mathrm { e } } x \right) ^ { 1 / 2 } } { x \left( a - \left( \log _ { \mathrm { e } } x \right) ^ { 3 / 2 } \right) ^ { 2 } } d x = 1 , \quad a \in ( - \infty , 0 ) \cup ( 1 , \infty )$$
Which of the following statements is/are TRUE ?\\
(A) No $a$ satisfies the above equation\\
(B) An integer $a$ satisfies the above equation\\
(C) An irrational number $a$ satisfies the above equation\\
(D) More than one $a$ satisfy the above equation