The value of the integral
`overset(1)underset(1//3)int((x-x^(3))^(1//3))/(x^(4))dx` is

Explanation

`I=overset(1)underset(1//3)int((x-x^(3))^(1//3))/(x^(4))dx`


Put `x=sintheta=>dx=costhetad theta`


when `x=1/3,theta=sin^(1/3)` and when `x=1,theta=pi/2`


=>`I=int_(sin^-1(1/3))^(pi/2) (sintheta-sin^3theta)^(1/3)/(sin^4theta)costhetad theta`


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