Chapter5 The Indefinite Integral

这是一篇关于Chapter5 The Indefinite Integral 的思维导图，不定积分和定积分间的关系，由微积分基本定理确定。

Chapter5 The Indefinite Integral

• 5.1 The Concept and the Properties of the Indenfinite Integral
  • The Concepts of the Prinmitove Functionand the Indefinite Integral
    • F'(x)=f(x)
    • ∫f(x)dx=F(x)+C (F(x) is a primitive
    • Existence Theorem for the Primitive Function:
      • continuous functions have primitive function certainly.
  • Basic Formulas of Integrals
  • The Properties of the Indefinite Integral
    • Property 1
      • ∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx or ∫[f(x)-g(x)]dx=∫f(x)dx-∫g(x)dx
    • Property 2
      • ∫kf(x)dx=k∫f(x)dx (k is a nonzero constant)
• Integration
  • 5.2 Integration by Substitution
    • The Substitution Rule 1
    • The Substitution Rule 2
  • 5.3 Integration by Parts
    • ∫uv'dx=uv-∫u'vdx
  • 5.4 The Indefinite Integral of the Rational Function
    • The Indefinite Integral of the Rational Function
    • The Indefinite Integral of the Rational Function with Trigonometric Function
    • The Indefinite Integral of the Simple Irrational Function