Mathematical formulas

Calculus II

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Sections

1Notation, domains and conventions
2Indefinite integral and properties
3Definite integral and Fundamental Theorem of Calculus
4Substitution method
5Integration by parts
6Trigonometric integrals
7Trigonometric substitution and quadratic radicals
8Rational functions and partial fractions
9Improper integrals
10Applications of the integral
11Numerical integration
12Parametric curves
13Polar coordinates
14Sequences and series
15Power series and Taylor series
16Elementary differential equations
17Guide to choosing a method
AAppendix A: extensive table of antiderivatives
BAppendix B: useful equivalences

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Calculus II
Appendix A: extensive table of antiderivatives

Section A

Appendix A: extensive table of antiderivatives

In this section

A.1. Basic integration formulas
A.2. Trigonometric integrals
A.3. Inverse trigonometric integrals
A.4. Exponential and logarithmic integrals
A.5. Hyperbolic integrals
A.6. Integrals with $2 a u - u^{2}$
A.7. Integrals with $a^{2} + u^{2}$
A.8. Integrals with $a^{2} - u^{2}$
A.9. Integrals with $u^{2} - a^{2}$
A.10. Integrals with $a + b u$

The following formulas come from the original catalog, with clarified notation and general restrictions added.

Usage rule: in addition to the conditions written next to each family, it is assumed that all denominators are nonzero and that the expressions are within the real domain. The identities apply on connected intervals of the domain.

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