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BITSAT2023MathematicsIndefinite IntegrationActual

If e ^ x (1+ x ) dx 1+ x = e ^ x f ( x )+ C , then f ( x ) is equal to

Options

  1. Ax 2
  2. Bx 2
  3. Cx 2
  4. Dx 2

Correct answer

C. x 2

Step-by-step solution

e^x (1+ x) (1+ x) d x = e^x [ 1 2 ^2 x 2 + x 2 ] d x = 1 2 e^x ^2 x 2 d x+ e^x x 2 d x = e ^ x x 2 + C But I = e ^ x f ( x )+ C (given) f ( x )= x 2

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