List of integrals of irrational functions

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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 constant of integration is omitted for brevity.

Integrals involving r = a2 + x2[edit]

Integrals involving s = x2a2[edit]

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

Here , where the positive value of is to be taken.

Integrals involving u = a2x2[edit]

Integrals involving R = ax2 + bx + c[edit]

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

Integrals involving S = ax + b[edit]