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If the integrand is a rational function of `x` and fractional power 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)`, where `m` is L.C.M. of fractional powers of `(ax+b)/(cx+d)`.
If ` int(dx)/((x-1)^(3//4)(x+2)^(5//4))=A((x-1)/(x+2))^(1//4)+C` then

A

`A=(1)/(3)`

B

`A=(2)/(3)`

C

`A=(3)/(4)`

D

`A=(4)/(3)`

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Knowledge Check

  • 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
    `2/3`
    B
    `-3/2`
    C
    `1/3`
    D
    `1/2`

  • If int(dx)/((x-sqrt(x^(2)-1))^(2))=Ax^(3)+Bx^(2)+Cx+D(x^(2)-1)^(3//2)+E , then

    A
    `A=(2)/(3), B=0, C=-1`
    B
    `A=(1)/(3), B=0, D=(2)/(3)`
    C
    `A=D=(2)/(3), B=0, C=-2`
    D
    none of these

  • If int(dx)/((x-sqrt(x^(2)-1)))=Ax^(3)+Bx^(2)+Cx+D(x^(2)-1)^(3//2)+E , then

    A
    `A=(2)/(3),B=0,C=-1`
    B
    `A=(1)/(3),B=0,D=(2)/(3)`
    C
    `A=D=(2)/(3),B=0,C=-2`
    D
    none of these