If ∫ ( x - 1 ) 2 x 2 + 1 2 d x = tan - 1 x + g x + k , then g ( x ) is equal to

Question

If ∫ ( x - 1 ) 2 x 2 + 1 2 d x = tan - 1 x + g x + k , then g ( x ) is equal to, tan − 1 ⁡ x 2, 1 x 2 + 1, 1 2 x 2 + 1, 2 x 2 + 1

MARKS App · Accepted Answer

Given that ∫ x - 1 2 x 2 + 1 2 d x = ∫ x 2 + 1 - 2 x x 2 + 1 2 d x = ∫ x 2 + 1 x 2 + 1 2 d x - ∫ 2 x x 2 + 1 2 d x = ∫ 1 x 2 + 1 d x - ∫ 2 x x 2 + 1 - 2 d x We know that ∫ f ' x f x n d x = f x n + 1 n + 1 + c = tan - 1 x + x 2 + 1 - 1 + c So g x = 1 x 2 + 1 .

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