If the integrand is a rational function ...

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

`2/3`

`-3/2`

`1/3`

`1/2`

Text Solution

Verified by Experts

The correct Answer is:

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

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