Integrating complex functions can feel like a really big challenge, almost like trying to find your way through a maze of complicated math. But this is where substitution comes in! However, it also has its own set of difficulties.

1. Understanding the Idea: Substitution is all about making a hard integral easier by changing the variables we use. While this can help a lot, choosing the right substitution can be tough. If you pick the wrong one, it can make the integral even harder to solve.

2. Finding Substitutions: One helpful trick is to look for patterns in the integral. For example, if you see an integral like $\int f(g(x)) g'(x) \, dx$, you might want to try $u = g(x)$ as a substitution. But figuring out if this substitution works can take practice and might make you feel frustrated when dealing with tricky functions.

3. Making the Substitution: After choosing a good substitution, rewriting the integral involves several steps. This can lead to mistakes in algebra. For instance, when you change $dx$ to $du$, you might forget about the limits of integration or mix up the new boundaries, which can mess up the final answer.

4. Going Back to the Original Variable: After you solve the integral using the new variable, returning to the original variable can be tricky. If you didn’t handle the transformation carefully, it can feel like a hard struggle to get the right answer.

Even with these challenges, substitution can make integrals easier if you keep a few things in mind:

• Practice: The more you practice, the better you'll get at noticing when substitutions work.
• Recognizing Patterns: Learning how to quickly spot integrals that are great for substitution can help a lot.
• Step-by-Step Method: Breaking the process into smaller parts can help you feel less overwhelmed.

In short, while substitution can seem difficult and sometimes frustrating, with careful attention and regular practice, it can become a powerful tool for making integrals in calculus much simpler.