Set $y\=3 x-2$ so that $\mathrm{dy}\=3 \mathrm{dx}$ and $\mathrm{dx}\=\mathrm{dy}\/3$. Under this change of variable, the given indefinite integral becomes

 $\int \sqrt{y}\frac{\mathit{\ⅆ}y}{3}\=\frac{1}{3}\int y^{1\/2} \mathit{\ⅆ}y\=\frac{1}{3} \frac{y^{3\/2}}{3\/2}\=\frac{2}{9}{\left(3 x-2\right)}^{3\/2}$ 

Of course, there are settings in which the addition of an arbitrary constant is deemed essential.

Figures 4.4.1(a), 4.4.1(b), and Table 4.4.1(a) detail how to obtain a stepwise solution interactively via the  tutor.

Table 4.4.1(a) lists the complete stepwise solution available from the  tutor.

After the antiderivative $F\left(y\right)$ is found, the Revert rule returns $F\left(y\left(x\right)\right)$, that is, reverses the substitution after the integral has been evaluated.

It is interesting to note that Maple might make a different substitution, as per Table 4.4.1(b) where the Context Panel's Student Calculus1≻All Solution Steps option is applied to the indefinite integral.

Maple has made the substitution $u^2\=3 x-2$, so that $u\=\sqrt{3 x-2}$ and $2 u \mathrm{du}\=3 \mathrm{dx}$. Thus, $\mathrm{dx}\=\frac{2}{3}u \mathrm{du}$ and the new integrand is $u \left(\frac{2}{3}u\right)\=\frac{2}{3}{u}^2$. Of course, the final results for the two approaches will agree, but some of the intermediate steps will not.

There is a change command in the Rules section of the Student Calculus1 package, and a Change command in the IntegrationTools package. The change command in the Calculus1 package is essentially the one embedded in the Integration Methods tutor.

The change command is part of a larger structure of stepwise solving tools best left to the implementation in the tutors; the Change command is more useful in a "production" mode where results are of uppermost importance.