The value of b > 3 for which 12 ∫ 3 b 1 x 2 - 1 x 2 - 4 d x = log e 49 40 , is equal to _____.

Step-by-step solution

Given 12 × ∫ 3 b 1 d x x 2 - 4 x 2 - 1 = ln 49 40   &   4   b > 3 ⇒ By Using partial fraction 1 x 2 - 4 x 2 - 1 = 1 3 1 x 2 - 4 - 1 x 2 - 1 ⇒ 12 3 ∫ 3 b 1 x 2 - 4 - 1 x 2 - 1 = ln 49 40 ⇒    4 1 4 log x - 2 x + 2 - 1 2 log x - 1 x + 1 3 b = ln 49 40 ⇒    log b - 2 b + 1 2 b + 2 b - 1 2 × 5 4 = log 49 40 ⇒    b - 2 b + 1 2 b + 2 b - 1 2 × 5 4 = 49 40 ⇒ b - 2 b + 1 2 b + 2 b - 1 2 = 49 50