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COMEDK2024MathematicsIndefinite IntegrationActual

f^ (x) f(x) (f(x)) d x is equal to

Options

  1. A( f(x))+C
  2. B1 ( f(x)) +C
  3. Cf(x) f(x) +C
  4. Df(x) f(x)+C

Correct answer

A. ( f(x))+C

Step-by-step solution

Let I = f'(x) f(x) (f(x)) dx . Substitute u = (f(x)) . Then, du = 1 f(x) f'(x) dx = f'(x) f(x) dx . Substituting these into the integral, we get I = 1 u du . Integrating with respect to u , we obtain I = |u| + C . Substituting back u = (f(x)) , we get I = | (f(x))| + C . Answer: ( f(x))+C

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