When students use substitution in integration, they often make some common mistakes. Let’s break them down:

1. Picking the Wrong Substitution: If you choose a bad substitution, it can make the problem harder. Try to pick one that makes the expression easier to work with.

2. Overlooking the Derivative: It's really important to change the variable when you substitute. If you have $u = g(x)$, you also need to change $dx$. You'll do this using the formula $dx = \frac{du}{g'(x)}$.

3. Forgetting to Change Back: After you finish integrating with respect to $u$, don’t forget to switch back to your original variable.

Here's an example:

For $\int 2x \cdot x^2 \, dx$, if you let $u = x^2$, you need to remember to use this substitution in your calculations to get the right answer!

By keeping these tips in mind, you can avoid common pitfalls when using substitution in integration. Good luck!