If ∫ d x x 3 1 + x 6 2 3 = x f x 1 + x 6 1 3 + C , where C is a constant of integration, then the function f x is equal to

Question

If ∫ d x x 3 1 + x 6 2 3 = x f x 1 + x 6 1 3 + C , where C is a constant of integration, then the function f x is equal to, 3 x 2, - 1 2 x 3, - 1 6 x 3, - 1 2 x 2

MARKS App · Accepted Answer

We have, ∫ d x x 3 1 + x 6 2 3 = x f x 1 + x 6 1 3 + C Now, I = ∫ d x x 7 1 x 6 + 1 2 3 Put, t = 1 x 6 + 1 ⇒ d t = - 6 x 7 d x ∴ I = - 1 6 ∫ d t t 2 3 = - 1 2 t 1 3 + C , where C is the constant of integration = - 1 2 1 x 6 + 1 1 3 + C = - 1 2 1 + x 6 1 3 x 2 + C ∴ f x = - 1 2 x 3

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