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MHT CET202314 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

2 x (1- 3 2 x ) e ^ ^2 x+ ^3 x ~d x=

Options

  1. Ae ^ ^2 x+ ^3 x + c , where c is a constant of integration.
  2. B- e ^ - ( ^2 x+ ^3 x ) + c , where c is a constant of integration.
  3. Ce ^ - ( ^2 x+ ^3 x )^2 + c , where c is a constant of integration.
  4. De ^ ^2 x+ x + c , where c is a constant of integration.

Correct answer

B. - e ^ - ( ^2 x+ ^3 x ) + c , where c is a constant of integration.

Step-by-step solution

aligned & Put ^2 x+ ^3 x= t & (2 x x-3 ^2 x x ) d x= dt & ( 2 x- 3 2 2 x x ) d x= dt & 2 x (1- 3 2 x ) d x= dt & 2 x (1- 3 2 x ) d d x & = 1 e ^ t dt ^2 x+ ^3 x & = e ^ - t dt & =- e ^ - t + c & =- e ^ - ( ^2 x+ ^3 x ) + c aligned

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