To evaluate the indefinite integral \(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x\), we can use the method of substitution. Let \(u = 2x - 3\). Then, \(\mathrm d u = 2 \mathrm d x\), and the integral becomes:

\(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x = \int u^{\frac{2}{3}} \mathrm d u\)

Using the power rule for integration, we have:

\(\int u^{\frac{2}{3}} \mathrm d u = \frac{3}{5}u^{\frac{5}{3}} + C\)

Substituting back for \(u = 2x - 3\), we get:

\(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x = \frac{3}{5}(2x - 3)^{\frac{5}{3}} + C\)