Using the substitution technique in integrals can be tough for many Year 12 students. This often leads to confusion at different steps. Let’s break down the tricky parts:

1. Finding the Right Substitution: Picking the right substitution can be hard. You need to find a function, called $u = g(x)$, that makes the integral easier. But sometimes, this choice isn’t obvious.

2. Adjusting the Limits: When you’re working with definite integrals (which have set limits), you need to change these limits according to your substitution. Forgetting this step can mess up your answers.

3. Differentiating the Substitution: Students often find it challenging to differentiate. This means expressing $dx$ in terms of $du$ correctly. This can lead to a tricky expression that’s easy to get wrong.

4. Going Back to the Original Variable: After you’ve integrated with respect to $u$, getting back to the original variable, $x$, can be tough. This is especially true if the inverse of your substitution isn’t easy to find.

Even with these challenges, students can get better at this. Practicing different problems and focusing on common techniques, like choosing $u = g(x)$ for tricky functions, can help them understand better. Also, working through examples with help can strengthen their skills.