This post features a clean, side-by-side breakdown of the Tabular Method and traditional Integration by Parts (IBP) so you can finally understand when and how to use each. This reference image is designed for calculus students preparing for exams or tackling long integration problems.

Integration by Parts is a method for solving integrals of products of functions. The Tabular Method is a streamlined shortcut when IBP must be applied multiple times. In this visual, you'll see how both methods handle integrals like:

• ∫ x·eˣ dx using Integration by Parts

• ∫ x²·e²ˣ dx using the Tabular Method

You’ll also get a charted layout showing how derivatives and integrals alternate with sign changes, allowing quick expansion into a complete solution. This method is especially useful when one function reduces to zero through repeated differentiation, making it perfect for polynomials times exponentials or trig functions.

This visual is taken directly from my best-selling PDF crash course for STEM majors. If you’re a college student studying calculus or applied math:

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