If ∫ d x x + 1 2 x 2 + 2 x + 2 = A x + 1 + B tan - 1 ⁡ x + 1 + C , where A and B are constants and C is the constant of integration, then A - B is equal to

Question

If ∫ d x x + 1 2 x 2 + 2 x + 2 = A x + 1 + B tan - 1 ⁡ x + 1 + C , where A and B are constants and C is the constant of integration, then A - B is equal to,

MARKS App · Accepted Answer

∫ d x x + 1 2 x 2 + 2 x + 2 = ∫ x 2 + 2 x + 2 - x 2 + 2 x + 1 x 2 + 2 x + 1 x 2 + 2 x + 2 d x = ∫ d x x + 1 2 - ∫ d x x + 1 2 + 1 = - 1 x + 1 - tan - 1 ⁡ x + 1 + C So A = B = - 1 Hence, A - B = 0

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