1. Antidifferentiation by Substitution
Chapter 7
Differential Equations and Mathematical Modeling
Section 7.2
Antidifferentiation by
Substitution

2. What you’ll learn about
Indefinite integrals
Properties of indefinite integrals
Antiderivative formulas arising from known derivatives
Leibniz notation (differentials) in integrals
Using substitution to evaluate indefinite integrals
Using substitution to evaluate definite integrals
… and why
Antidifferentiation techniques were historically
crucial for applying the results of calculus.

3. Indefinite Integral

4. Example Evaluating an Indefinite Integral

5. Properties of Indefinite Integrals

6. Power Functions

7. Trigonometric Formulas

8. Exponential and Logarithmic Formulas

9. Example Paying Attention to the Differential

10. Example Using Substitution

11. Example Using Substitution

12. Example Setting Up a Substitution with a Trigonometric Identity

13. Example Evaluating a Definite Integral by Substitution