If the integrand is a rational function of x and fractional powers of a linear fractional…

If the integrand is a rational function of x and fractional powers of a linear fractional function of the form \(\frac{a x+b}{c x+d}\). Then rationalization of the integral is affected by the substitution \(\frac{\mathrm{ax}+\mathrm{b}}{\mathrm{cx}+\mathrm{d}}=\mathrm{t}^{\mathrm{m}},\)where m is the L.C.M. of fractional powers of \(\frac{a x+b}{c x+d}\).
If \(I=\int \frac{(2 x-3)^{1 / 2}}{(2 x-3)^{1 / 3}+1} d x=3\left[\frac{1}{7}(2 x-3)^{7 / 6}-\frac{1}{5}(2 x-3)^{5 / 6}+\right.\)
\(\left.\frac{1}{3}(2 \mathrm{x}-3)^{1 / 2}-(2 \mathrm{x}-3)^{1 / 6}+\mathrm{g}(\mathrm{x})\right]-1\) then g (x) is equal to