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 &#8747; d x x 3 1 + x 6 2 3 &#160; = x f x 1 + x 6 1 3 + C , where C is a constant of integration, then the function f x is equal to

Aicharya · Accepted Answer

We have, &#8747; d x x 3 1 + x 6 2 3 = x f x 1 + x 6 1 3 + C Now, I = &#8747; d x x 7 1 x 6 + 1 2 3 Put, t = 1 x 6 + 1 &#8658; d t = - 6 x 7 d x &#8756; I = - 1 6 &#8747; 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 &#8756; f x = - 1 2 x 3

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…

Solution

If &#8747; d x x 3 1 + x 6 2 3 &#160; = x f x 1 + x 6 1 3 + C , where C is a constant of integration, then…

Solution

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…