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AP EAMCET2001MathematicsIndefinite Integration

(x+1)^2 e^x d x is equal to

Options

  1. Ax e^x+C
  2. Bx^2 x^x+C
  3. C(x+1) e^x+C
  4. D(x^2+1 ) e^x+C

Correct answer

D. (x^2+1 ) e^x+C

Step-by-step solution

aligned & (x+1)^2 e^x d x &=(x+1)^2 e^x- 2(x+1) e^x d x &=(x+1)^2 e^x-2(x+1) e^x+2 e^x+C &=e^x [x^2+2 x+1-2 x-2+2 ]+C &=e^x [x^2+1 ]+C aligned

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