Lists of integrals

Topics in Calculus

Fundamental theorem | Function | Limits of functions | Continuity | Calculus with polynomials

Differentiation

Product rule | Quotient rule | Chain rule | Implicit differentiation | Taylor's theorem

Integration

Integration by substitution | Integration by parts | Integration by trigonometric substitution | Solids of revolution | Integration by disks | Integration by cylindrical shells | Lists of integrals

Vector Calculus

Vector | Vector field | Matrix | Partial Derivative | Gradient | Flux | Divergence | Divergence Theorem | Del | Curl | Stokes' Theorem

Tensor Calculus

Tensor | Tensor field | Tensor product | Exterior power | Exterior Derivative | Covariant derivative | Manifold

See the following pages for lists of integrals:

• List of integrals of rational functions
• List of integrals of irrational functions
• List of integrals of trigonometric functions
• List of integrals of hyperbolic functions
• List of integrals of exponential functions
• List of integrals of logarithmic functions
• List of integrals of arc functions
• List of integrals of area functions

Also see table of integrals for the most common integral functions.

Other lists of integrals

Gradshteyn and Ryzhik contains a large collection of results. Other useful resources include the CRC Standard Mathematical Tables and Formulae and Abramowitz and Stegun. A&S contains many identities concerning specific integrals, which are organized with the most relevant topic instead of being collected into a separate table.

There are several web sites which have tables of integrals, and at least two which offer integrals on demand.

References

• Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.

• Alan Jeffrey and Daniel Zwillinger, editors. Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, sixth edition. Academic Press, 2000. ISBN 0-12-294757-6. (Several previous editions as well.)

• Daniel Zwillinger. CRC Standard Mathematical Tables and Formulae, 31st edition. Chapman & Hall/CRC Press, 2002. ISBN 1584882913. (Many earlier editions as well.)