📚 Key Concepts
Integration as Inverse of Differentiation- If F'(x) = f(x), then ∫f(x)dx = F(x) + C
- Integration constant (C)
- Indefinite integral represents family of curves
Standard Integration Formulas- ∫xⁿdx = (xⁿ⁺¹)/(n+1) + C, n ≠ -1
- ∫(1/x)dx = ln|x| + C
- ∫eˣdx = eˣ + C
- ∫sin x dx = -cos x + C
- ∫cos x dx = sin x + C
- ∫sec² x dx = tan x + C
🎯 Key Formulas
Integration by SubstitutionIntegration by Parts: ∫udv = uv - ∫vduPartial Fractions:- Proper/Improper fractions
- Types of factors (linear, repeated, quadratic)
Definite Integration:- ∫ₐᵇf(x)dx = F(b) - F(a)
- Properties of definite integrals
⚠️ Common Mistakes to Avoid
Forgetting integration constantWrong substitutionSign errors in parts formulaIncorrect limits in definite integrationWrong decomposition in partial fractionsMissing absolute value in ln integration
📖 Knowledge Prerequisites
Differentiation rulesAlgebraic fractionsTrigonometric identitiesExponential/logarithmic functionsFactorization techniques
💡 Tips for Students
Learn standard integrals thoroughlyPractice substitution patternsCheck answers by differentiationDraw diagrams for definite integralsBreak complex integrals into simpler partsPay attention to domain restrictions
👉 Practice Recommedations
Basic indefinite integralsIntegration by substitutionIntegration by partsPartial fraction problemsDefinite integral evaluationsMixed integration methodsApplication problems
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