This post features a step-by-step image comparison of the Tabular Method and Integration by Parts (IBP), designed for students taking calculus, especially during exams where speed and clarity matter.

Integration by Parts is a classic technique used for integrals involving products of functions. The Tabular Method is a faster, more structured version of IBP that shines when integration by parts would otherwise need to be done repeatedly—like when integrating polynomial-exponential or polynomial-trig combinations.

In this visual guide:

• You’ll first see a basic IBP example: ∫ x·eˣ dx.

• Then it walks through a more complex case: ∫ x²·e²ˣ dx using the Tabular Method.

• The tabular approach uses alternating signs and a simple derivative/integral chart to produce results much faster and cleaner than standard IBP.

These reference visuals are pulled straight from the Ultimate Crash Course for STEM Majors, an all-in-one learning tool packed with 800+ pages of explanations, diagrams, and problem walkthroughs for calculus, algebra, and beyond.

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