Calculus I (MATH 101) Integration Techniques Practice Problems (u-Sub, By Parts, Trig Sub, Partial Fractions)
Stanford University
Calculus I (MATH 101) | Practice Problems

Overview
A Calculus exam-season practice set focused on choosing the right integration technique quickly: substitution, integration by parts, trig substitution, and partial fractions with the common patterns students miss under time pressure.

Key topics
•u-sub recognition patterns (chain rule in reverse)
•integration by parts setup and picking u and dv
•trig substitution triangles and when it applies
•partial fraction decomposition basics
•quick checks by differentiating your answer

Suggested study tasks
•solve 8 u-sub integrals with clean substitutions
•solve 8 integration-by-parts problems (including repeated by parts)
•solve 6 trig substitution integrals and back-sub correctly
•decompose and integrate 8 partial fraction problems
•write a 1-page technique decision tree for finals

Common pitfalls
•forgetting to change dx and bounds in substitution
•choosing u poorly in integration by parts
•losing algebra steps during trig back-substitution
•decomposing partial fractions with missing terms
•skipping a derivative check and carrying sign errors