Calculus I (MATH 101) Integration Techniques Cheat Sheet: u-Sub, Parts, and Trig Substitution
University of California, Berkeley
Calculus I (MATH 101) | Study Guide

Overview
A compact integration techniques guide for common Calc I exam integrals and setup decisions.

Key topics
•u-substitution patterns
•integration by parts setup
•trig identities and trig integrals
•trig substitution triangles
•definite integrals with substitution

Suggested study tasks
•choose a method for 12 mixed integrals
•set up u-sub with correct du and new bounds
•apply LIATE to pick u in parts
•rewrite trig powers using identities

Common pitfalls
•forgetting to change bounds on definite integrals
•choosing u that makes the integral harder
•algebra mistakes in trig substitution triangles
•losing a negative sign in du