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NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

If the value of integral ∫ d x x + x 2 - 1 2 = a x 3 - x + b x 2 - 1 1 b + C , (where, C is the constant of integration), then a × b is equal to

Options

A1
B4 9
C2
D9 4

Correct answer

B. 4 9

Step-by-step solution

∫ x - x 2 - 1 2 d x = ∫ x 2 + x 2 - 1 - 2 x x 2 - 1 d x = 2 x 3 3 - x + 2 3 x 2 - 1 3 2 + C ⇒ a = b = 2 3

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