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The integral of $e^{2x}$ can be expressed as

where $C$ represents the constant of integration.

To compute the integral of $e^{2x}$, we typically rely on the power rule of integration, which states that

However, since $e^{2x}$ does not match the form $x^n$, we will employ a different technique: substitution.

We can let $u = 2x$. Then, we differentiate to find $\frac{du}{dx} = 2$, which implies that

By substituting these into the integral, we have:

In summary, to find the integral of $e^{2x}$, we perform a substitution by letting $u = 2x$. This transforms the integral into

which is straightforward to evaluate. The final result is

where $C$ is a constant of integration. This method illustrates how substitution can effectively simplify and solve integrals that do not conform to standard forms.