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If ∫ dx x - 1 3 / 4 x + 2 5 / 4 = k x - 1 x + 2 1 / 4 + c , then the number of divisors of 30 k is

Correct answer

8

Step-by-step solution

I = ∫ dx x - 1 x + 2 4 x + 2 2   put   x - 1 x + 2 = t On solving, we get, I = 4 3 x - 1 x + 2 1 4 + c k = 4 3 ⇒ 3 0 k = 4 0 = 2 3 × 5 1 Hence, total divisors are   4 × 2   =   8

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