Let ∫ d x x 2 + 1 - x = f x + C such that f 0 = 0 and C is the constant of integration, then the value of f 1 is

Question

Let ∫ d x x 2 + 1 - x = f x + C such that f 0 = 0 and C is the constant of integration, then the value of f 1 is, 1 2 + 1 2 ln ⁡ 1 + 2, 1 2 + 1 2 ln ⁡ 1 + 2, 1 2 + 1 2 ln ⁡ 2 + 1, 1 2 + 1 2 1 + ln ⁡ 1 + 2

MARKS App · Accepted Answer

∫ x 2 + 1 + x 1 d x ∫ x 2 + 1 d x + ∫ x d x = x 2 x 2 + 1 + 1 2 ln ⁡ x + x 2 + 1 + x 2 2 + C f x = x 2 x 2 + 1 + 1 2 ln ⁡ x + 1 x 2 + 1 + x 2 2 f 0 = 0 f 1 = 2 2 + 1 2 ln ⁡ 1 + 2 + 1 2 = 1 2 + 1 2 1 + ln ⁡ 1 + 2

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