Home
Class 12
MATHS
If the integrand is a rational function ...

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)`.
`int(dx)/((x+1)^(2//3)(x-1)^(4//3))=k[(1+x)/(1-x)]^(1//3)+C` then

A

`2/3`

B

`-3/2`

C

`1/3`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
(1) Put `(2x-3)^(1/6)=t`
(2) Put `(x+1)/(1-x)=t^(3)`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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)sqrt(1-x^(2)))=ksqrt((x+1)/(1-x))+C then

Find the inverse of the function f(x) = (ax+b)/(cx-a) , which is a bijection.

int_0^9{sqrt(x)}dx , where {x} denotes the fractional part of x , is 5 (b) 6 (c) 4 (d) 3

int_1^4(x-0. 4)dx equals (where {x }is a fractional part of (x) (a) 13 (b) 6.3 (c) 1.5 (d) 7.5

Evaluate the following limits : Lim_( x to 0 )(ax +b)/(cx +d)

If y =(ax +b)/( cx + d) , then prove that 2y_1y_3=3(y_2)^2

int(ax^3+bx^2+cx+d)dx

If 1/(x^(4)+x^(2)+1)=(Ax+B)/(x^(2)+x+1)+(Cx+D)/(x^(2)-x+1) " then "C+D=

(3x^(2)+x+1)/((x-1)^(4))=(A)/(x-1)+(B)/((x-1)^(2))+(C)/((x-1)^(3))+(D)/((x-1)^(4)) then A+B-C+D=