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"If"int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)...

`"If"int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)(1+x^(6))^(1/3)+C` where, C is a constant of integration, then the function f(x) is equal to

A. ` ( 3 ) /( x ^ 3 ) `
B. ` - ( 1 ) / ( 2x ^ 3 ) `
C. `- ( 1 ) / ( 2 x ^ 2 ) `
D. ` - (1 )/(6x ^ 3 ) `

A

` ( 3 ) /( x ^ 3 ) `

B

` - ( 1 ) / ( 2x ^ 3 ) `

C

`- ( 1 ) / ( 2 x ^ 2 ) `

D

` - (1 )/(6x ^ 3 ) `

Text Solution

AI Generated Solution

To solve the given problem, we start with the equation: \[ \int \frac{dx}{x^3 (1+x^6)^{2/3}} = x f(x) (1+x^6)^{1/3} + C \] ### Step 1: Simplify the Integral We can rewrite the integral on the left-hand side: ...
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