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 = √a2 + x2
Integrals involving s = √x2 − a2 Assume x2 > a2 (for x2 < a2, see next section):
Integrals involving u = √a2 − x2
Integrals involving R = √ax2 + bx + c Assume (ax2 + bx + c) cannot be reduced to the following expression (px + q)2 for some p and q.
Integrals involving S = √ax + b
References