Select all expressions metching the value of indefinite integral int (2x)/(3)(3x^2-1)dx (x^2)/(3)(x^3-x)+C (x^2)/(3)(x^2-1)+C (x^4)/(2)-(x^2)/(3)+C

To find the indefinite integral of the given expression, we can use the power rule for integration.<br /><br />The power rule states that the integral of x^n dx is (x^(n+1))/(n+1) + C, where C is the constant of integration.<br /><br />Let's apply the power rule to each term in the expression:<br /><br />$\int \frac {2x}{3}(3x^{2}-1)dx$<br /><br />= $\int \frac {2x}{3} \cdot 3x^{2} dx - \int \frac {2x}{3} \cdot 1 dx$<br /><br />= $\int 2x^{3} dx - \int \frac {2x}{3} dx$<br /><br />= $\frac {2}{4}x^{4} - \frac {2}{3}\cdot\frac {1}{2}x^{2} + C$<br /><br />= $\frac {x^{4}}{2} - \frac {x^{2}}{3} + C$<br /><br />Therefore, the correct answer is $\frac {x^{4}}{2} - \frac {x^{2}}{3} + C$.