Question

If the integrand is a rational function of `x` and fractinal powers of a linear fractional of the form `(Ax+B)/(Cx+D)`, then rationalization of the integral is affected by the substitution `(Ax+B)/(Cx+D)=t^(m)`
If `int (dx)/(root(3)((x+1)^(2)(x-1)^(4)))=Kroot(3)((1+x)/(1-x))+C`,
Then `K` is equal to
A. `tan^(-1)(2x-3)^(1/6)`
B. `(2x-3)^(1/6)`
C. `3tan^(-1)(2x-3)^(1/6)`
D. `4(2x-3)^(1/6)`

Answer 1

Correct Answer - A
(1) Put `(2x-3)^(1/6)=t`
(2) Put `(x+1)/(1-x)=t^(3)`