If f ( x ) is a polynomial function of the n th degree, then e^ x f(x) d x is equal to

Mathematics · JEE Advanced · NTA Exams — Integral Calculus

1. e^x {f (x) – f’ (x) – f” (x) – f”’ (x) – ... – (– 1)ⁿ fⁿ (x)}
2. e^x {f (x) – f’ (x) + f” (x) – f”’ (x) + ... + (– 1)ⁿ fⁿ (x)}
3. e^x {f (x) – f’ (x) + f” (x) – f”’ (x) + ... + (1)ⁿ fⁿ (x)}
4. none of these

Answer

(B) e x f ( x ) – f’ ( x ) + f” ( x ) – f”’ ( x ) + ... + (– 1) n f n ( x )

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