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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)`.
If ` int(dx)/((x-1)^(3//4)(x+2)^(5//4))=A((x-1)/(x+2))^(1//4)+C` then

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)`

Text Solution

Verified by Experts

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