List of integrals of irrational algebraic functions

The following is a list of integrals (antiderivative functions) of irrational functions. For a complete list of integral functions, see lists of integrals. Throughout this article the integration variable and all parameters are assumed to be real numbers and the constant of integration is omitted for brevity.

Integrals involving r =

Integrals involving s =

Assume x² > a² (for x² < a², see next section):

• where the positive value of is to be taken.

Integrals involving u =

Integrals involving R =

Assume (ax² + bx + c) cannot be reduced to the following expression (px + q)² for some p and q.

Integrals involving S =

References

• (Several previous editions as well.)