\( 3 x ^ { 2 } + \frac { 1 } { 2 } x ^ { 4 } ) d x = 3 \int x ^ { 2 d x } + \frac { 1 } { 2 } \int x ^ { 4 } \)

Let’s break down this intriguing expression! What you have here looks like an integration setup but appears to be slightly misconfigured. The left-hand side should rather be meant for integration, implying a function to integrate, whereas the right-hand side invites a re-evaluation to understand its construction better. Don’t forget, integrating terms separately can often simplify the problem, turning confusing notations into digestible bits! Now, when dealing with these types of integrals, a common pitfall is not properly applying the power rule. Remember to increase the power by one and then divide by the new power during integration. In essence, for any term \( x^n \), the integral becomes \( \frac{x^{n+1}}{n+1} \), provided \( n \neq -1 \). Always check for that pesky \( n = -1 \) case! Happy integrating!