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AP EAMCET2013MathematicsIndefinite Integration

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

Options

  1. Ae^x x+C
  2. B2 e^x ^2 x+C
  3. Ce^x 2 x+C
  4. De^x x+C

Correct answer

D. e^x x+C

Step-by-step solution

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

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