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Integration by Parts: Tabular Method
AP Calculus BC · Unit 6 Integration Techniques
Learning Objectives
Apply the Tabular (aka "Tic-Tac-Toe") shortcut
Choose u: the function that simplifies upon differentiation
Choose dv: the function easy to integrate
Manage alternating signs (+, −, +, −, ...)
LIATE Rule (u Priority)
Logarithmic: ln(x), log(x)
Inverse Trig: arcsin, arctan
Algebraic: x², x³, polynomials
Trigonometric: sin(x), cos(x)
Exponential: eˣ, 2ˣ

Higher in the list → better choice for "u" (differentiating side).
Tags
integration by partstabular methodLIATE
INTEGRAL ∫ u · dv
How to Read the Table
1. Create two columns: "Differentiate" (u) and "Integrate" (dv)
2. Differentiate leftward until 0 (or pattern repeats)
3. Integrate rightward repeatedly
4. Alternating signs: +, −, +, −, ...
5. Each diagonal product is a term in the answer!