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AP EAMCET202317 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

e^ x (x ^3 x- x ) ^2 x d x=

Options

  1. Ae^ x (x- x)+C
  2. Be^ x (x- cosec x)+C
  3. Ce^ x (x+ x)+C
  4. De^ x (x+ cosec x)+C

Correct answer

A. e^ x (x- x)+C

Step-by-step solution

aligned & I= e^ x ( x ^3 x- x ^2 x ) d x & = e^ x (x x- x x) d x & = e^ x x x d x- e^ x x x d x & =x e^ x x d x- (1 e^ x x d x ) d x- & e^ x x d x- e^ x x ( x x d x) d x +C & =x e^ x - e^ x d x-e^ x x+ e^ x d x+C & e^ x (x- x)+C aligned

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