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KCET2013MathematicsIndefinite Integration

(x-1) e^ x (x+1)³ d x is equal to

Options

  1. Ae^ x x+1 +C
  2. Be^ x (x+1)² +C
  3. Ce^ x (x+1)³ +C
  4. Dx e^ x (x+1) +C

Correct answer

B. e^ x (x+1)² +C

Step-by-step solution

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

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