Wolfram Language is extremely flexible, and there are many ways to compute the solution for $y^{\prime }\left(x\right)=$ $6x$.

Use the $\mathrm{DSolveValue}$ function to compute solutions to ordinary differential equations.

For the given differential equation, the corresponding code is:

$\text{DSolveValue[y'[x]==}$ $6\mathrm{x}\text{,}$ $\text{y[x],}$ $\text{x]}$

The $\mathrm{DSolve}$ function can also be used to compute solutions to differential equations. Unlike $\mathrm{DSolveValue}$, it returns the solution as a list of rules of the form $\mathrm{y}\left(\mathrm{x}\right)\to \mathrm{sol}$. Therefore, a replacement rule needs to be applied before extracting the expression for the solution. The replacement rule can be done with $\mathrm{ReplaceAll}(/.$ $)$. Then, extract the solution with $\mathrm{First}$, $\mathrm{Part}$, $\mathrm{Extract}$ or any other equivalent function.

For the given differential equation, the corresponding Wolfram Language code is:

$\text{First[y[x]/.}$ $\text{DSolve[y'[x]==}$ $6\mathrm{x}\text{,}$ $\text{y[x],}$ $\text{x]]}$

The $\mathrm{Integrate}$ function can also be used to solve a simple differential equation like this one. However, the $\mathrm{GeneratedParameters}$ option must be included to ensure that the constant of integration is represented in the solution.

For the given differential equation, the corresponding Wolfram Language code is:

$\mathrm{Integrate}[6\mathrm{x},$ $\mathrm{x},$ $\mathrm{GeneratedParameters}\to \mathrm{C}]$

All of these approaches compute the solution of $y^{\prime }\left(x\right)=$ $6x$. However, keep in mind that there are many other ways to achieve the same result.