Cue Column:
- What is indefinite integration?
- What are the 6 main methods?
- How to choose the right method?
Note-Taking Area: Indefinite integration finds the antiderivative F(x) of f(x) such that F'(x) = f(x). The result always includes + C (constant of integration).
Six Core Methods:
- Direct Integration — Use standard formulas for basic functions
- Substitution — Recognize f(g(x))*g'(x) and set u = g(x)
- Integration by Parts — For products of different function types (LIATE)
- Partial Fractions — For rational functions with factorable denominators
- Trigonometric Techniques — Identities, reduction, product-to-sum
- Special Forms — [f+f'], trig substitution, completing the square
Method Selection Strategy:
- See a composite function with its derivative? -> Substitution
- Product of different types (log * polynomial)? -> By Parts
- Rational function? -> Partial Fractions (after long division if needed)
- Trig powers/products? -> Trig identities
- Square root of quadratic? -> Complete square + trig substitution or standard form
- times (function + its derivative)? -> Special formula
Summary Box: Integration is pattern recognition. The fastest path to solving JEE integrals is recognizing which method applies before computing. Practice identifying patterns over brute-force calculation.