# int (1-x)/((1+x)*(x+x^2+x^3)^(1/2)dx?

The integral can be first simplified a bit as $\int \frac{\left(1 - x\right) \mathrm{dx}}{\left(1 + x\right) {x}^{\frac{1}{2}} {\left(1 + x + {x}^{2}\right)}^{\frac{1}{2}}}$
Now multiply the numerator and denominator by ${\left(1 - x\right)}^{\frac{1}{2}}$
The result would be int((1-x)^(3/2) dx)/((1+x) x^(1/2) (1-x^3)^(1^/2 )