Evaluate $\int \frac{2-3x}{2+3x}\sqrt\frac{1+x}{1-x}dx$ Evaluate $$\int \frac{2-3x}{2+3x}\sqrt\frac{1+x}{1-x}d x$$
What substitution should I use ? $\sqrt\frac{1+x}{1-x}$ suggests $x=cos2\theta $ but its not useful in $\frac{2-3x}{2+3x}$

The substitution $t = \sqrt{\frac{1 + x}{1 - x}}$, that is, $$x = \frac{t^2 - 1}{t^2 + 1}, \qquad dx = \frac{4 t \,dt}{(t^2 + 1)^2},$$
rationalizes the integrand.
