Select all expressions matching the value of indefinite integral int x^2(1-2x+x^2)dx √ (x^3(6x^2-15x+10))/(30)+C (x^3)/(3)(-x^2+(x^3)/(3))+C -(x^4)/(2)+(x^5)/(5)+C (x^3)/(3)-(x^4)/(2)+(x^5)/(5)+C

To find the indefinite integral $\int x^{2}(1-2x+x^{2})dx$, we can first simplify the integrand by expanding the expression inside the parentheses:<br /><br />$x^{2}(1-2x+x^{2}) = x^{2} - 2x^{3} + x^{4}$<br /><br />Now, we can integrate each term separately:<br /><br />$\int x^{2} dx - 2\int x^{3} dx + \int x^{4} dx$<br /><br />Integrating each term, we get:<br /><br />$\frac{x^{3}}{3} - \frac{2x^{4}}{4} + \frac{x^{5}}{5} + C$<br /><br />Simplifying the expression, we have:<br /><br />$\frac{x^{3}}{3} - \frac{x^{4}}{2} + \frac{x^{5}}{5} + C$<br /><br />Therefore, the correct answer is $\frac{x^{3}}{3} - \frac{x^{4}}{2} + \frac{x^{5}}{5} + C$.