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BITSAT2024MathematicsDefinite IntegrationActual

The integral x^2 (x ^2 x+ x ) (x x+1)^2 d x is equal to

Options

  1. A- x^2 x x+1 +c
  2. B2 _e|x x+ x|+c
  3. C- x^2 x x+1 +2 _e|x x+ x|+c
  4. Dx^2 x^2 x-1 -2 _e|x x+ x|+c

Correct answer

C. - x^2 x x+1 +2 _e|x x+ x|+c

Step-by-step solution

(c) We note that d d x (x x+1)=x ^2 x+ x integrating by parts with x^2 as first function, we get aligned & I= x^2 x ^2 x+ x (x x+1)^2 d x & =x^2 (- 1 x x+1 )- 2 x (- 1 x x+1 ) d x & =- x^2 x x+1 +2 x x x x+ x d x & =- x^2 x x+1 +2 _e|x x+ x|+c & ( d d x (x x+ x)=x x ) aligned

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