Topic 4 of 6
Integration Techniques
Choose an antiderivative strategy from the structure of the integrand instead of guessing from a list.
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.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.03Calculus · Method guidePartial fractions: decompose before integratingTurn a proper rational function into simpler fractions whose antiderivatives are logarithmic or inverse-trigonometric.04Calculus · Decision guideChoosing the right trigonometric substitutionMatch a quadratic radical to a Pythagorean identity so the square root simplifies instead of becoming worse.05Calculus · Concept explainerImproper integrals are limits, not unusual notationReplace infinite bounds or unbounded integrands with limits before evaluating, then decide whether the result converges.