∫ 1 x 2 + 1 2 d x = ________

Question

∫ 1 x 2 + 1 2 d x = ________, tan - 1 ⁡ x - 1 2 x x 2 + 1 + c, 1 2 tan - 1 ⁡ x + x 2 x 2 + 1 + c, tan - 1 ⁡ x + 1 x 2 + 1 + c, tan - 1 ⁡ x + 1 2 x 2 + 1 + c

MARKS App · Accepted Answer

Let I = ∫ d x x 2 + 1 2 put x = t a n θ I = ∫ s e c 2 θ d θ s e c 4 θ = 1 2 ∫ 2 c o s 2 θ d θ I = 1 2 ∫ 1 - c o s 2 θ d θ 1 2 θ + 1 2 2 t a n θ 1 + t a n 2 θ I = 1 2 t a n - 1 x + 1 2 x 1 + x 2 + c

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