Calculus course topic
Integration Techniques
Choose an antiderivative strategy from the structure of the integrand instead of guessing from a list.
Core textbook
Begin with the complete Unit 3A map
Follow antiderivatives, signed accumulation, Riemann sums, the Fundamental Theorem, integration methods, numerical integration, improper integrals, review, exams, and published answer keys as one connected sequence.
Further exploration
Deep dives and extra articles
The core map above is the textbook. These articles are side trails: close readings of one method, a single integral, or a conceptual distinction that rewards more time and more examples.
Direct answers and concept explanations that make the structure visible.
Repeatable procedures with worked examples and checks.
01Calculus · Method guideu-substitution as the reverse Chain RuleReplace a repeated inner expression and its derivative with one variable so the antiderivative’s structure becomes visible.03Calculus · Method guidePartial fractions: decompose before integratingTurn a proper rational function into simpler fractions whose antiderivatives are logarithmic or inverse-trigonometric.06Calculus · Method guideIntegration by parts: choosing u and knowing when to repeatReverse the product rule, choose the factor that simplifies under differentiation, and recognize when the method should be repeated or abandoned.
Comparisons for the moments when several methods look possible.
02Calculus · Decision guideHow to choose an identity for a trigonometric integralThe parity of sine, cosine, secant, and tangent powers tells you what to save and what to convert.04Calculus · Decision guideChoosing the right trigonometric substitutionMatch a quadratic radical to a Pythagorean identity so the square root simplifies instead of becoming worse.