If ∫ 1 x 2 + 4 x 2 + 9 d x = A tan - 1 ⁡ x 2 + B tan - 1 ⁡ x 3 + C then A - B =

Question

If ∫ 1 x 2 + 4 x 2 + 9 d x = A tan - 1 ⁡ x 2 + B tan - 1 ⁡ x 3 + C then A - B =, 1 6, 1 30, - 1 30, - 1 6

MARKS App · Accepted Answer

Since 1 A B = 1 B - A 1 A - 1 B ⇒ ∫ 1 x 2 + 4 x 2 + 9 d x = ∫ 1 5 1 x 2 + 4 - 1 x 2 + 9 d x = 1 5 1 2 tan - 1 ⁡ x 2 - 1 3 tan - 1 ⁡ x 3 + C ⇒ A = 1 10 B = - 1 15 ⇒ A − B = 1 10 + 1 15 = 5 30 = 1 6

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