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If I = ∫ dx x 2 ⋅ 1 + x 2 = f x x + C ,   ∀x > 0 (where, C is the constant of integration) and f 1 = - 2 , then the value of f 3 is

Correct answer

2

Step-by-step solution

Given integral is I = ∫ d x x 3 1 + 1 x 2 Let 1 + 1 x 2 = t 2 ⇒ - 2 x 3 d x = 2 t d t ⇒ I = - ∫ t d t t = - x 2 - 1 x + C ⇒ f x = - x 2 + 1 ∴ f 3 = - 3 + 1 = 2

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