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MHT CET202312 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

( ( 1 x ) x )^2 ~d x=

Options

  1. Ax- x+ c , where c is a constant of integration
  2. B1 x - ( 1 x )+c , where c is a constant of integration.
  3. C1 x + ( 1 x )+ c , where c is a constant of integration.
  4. Dx+ x+ c , where c is a constant of integration.

Correct answer

B. 1 x - ( 1 x )+c , where c is a constant of integration.

Step-by-step solution

Let I = ( ( 1 x ) x )^2 ~d x Let 1 x = t 1 x^2 ~d x=- dt aligned I & =- ^2 t d t & = (1- ^2 t ) dt & = t - t + c & = 1 x - ( 1 x )+ c aligned

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