Evaluate. \[ \int x^{\frac{2}{3}} d x \]

Step 1 ：Given the integral \(\int x^{\frac{2}{3}} dx\)

Step 2 ：We can use the power rule for integration, which states that \(\int x^n dx = \frac{x^{n+1}}{n+1} + C\), where C is the constant of integration

Step 3 ：Here, n = 2/3. So, adding 1 to n gives us 2/3 + 1 = 5/3

Step 4 ：Substituting these values into the power rule gives us \(\int x^{\frac{2}{3}} dx = \frac{x^{\frac{5}{3}}}{\frac{5}{3}} + C\)

Step 5 ：To simplify the fraction, we can multiply the numerator and the denominator by 3 to get rid of the fraction in the denominator, which gives us \(\frac{3x^{\frac{5}{3}}}{5} + C\)

Step 6 ：So, the integral of \(x^{\frac{2}{3}}\) with respect to x is \(\boxed{\frac{3x^{\frac{5}{3}}}{5} + C}\)