Topic 4 of 6
Integration Techniques
Choose an antiderivative strategy from the structure of the integrand instead of guessing from a list.
01Method guideu-substitution as the reverse Chain RuleReplace a repeated inner expression and its derivative with one variable so the antiderivative’s structure becomes visible.02Decision 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.03Method guidePartial fractions: decompose before integratingTurn a proper rational function into simpler fractions whose antiderivatives are logarithmic or inverse-trigonometric.04Decision guideChoosing the right trigonometric substitutionMatch a quadratic radical to a Pythagorean identity so the square root simplifies instead of becoming worse.05Concept explainerImproper integrals are limits, not unusual notationReplace infinite bounds or unbounded integrands with limits before evaluating, then decide whether the result converges.