AI Tutor

Hello Alex! 👋 I'm your AP Calculus AB tutor. I see you're working on integration techniques today. What would you like help with?

Great question! Let me guide you through the decision process.

Use u-substitution when you see a composite function — the integrand contains a function and its derivative.

Use integration by parts when you have a product of two different types of functions (like polynomial × trigonometric, or polynomial × exponential).

Here's a quick test: Can you identify which technique you'd use for ∫ x·eˣ dx?

Exactly right! ✅ Since x·eˣ is a product of a polynomial (x) and an exponential (eˣ), integration by parts is the way to go.

Remember the formula: ∫ u dv = uv - ∫ v du

For this problem, what would you choose as u and dv? (Hint: Think about which function becomes simpler when differentiated)