A constant, such pi, that may be defined by the integral of an algebraic function over an algebraic domain is known as a period. The following is a list of some of the most common or interesting …

2 " a2x2 x3 sinaxdx = cosax (93) ! (98) ebx 1 cos(ax)dx ebx asinax = + bcosax ! ! sinaxsinhbxdx = (110) 1 !!!!!!!!!! ! sinhaxcoshbxdx = (112) 1 [ ] !!!!!!!!!!

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0 < φ < 2π.

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Basic Integrals 1. ∫ u n d u = u n + 1 n + 1 + C, n ≠ 1 2. ∫ d u u = ln | u | + C 3. ∫ e u d u = e u + C 4. ∫ a u d u = a u ln a + C 5. ∫ sin u d u = −cos u + C 6. ∫ cos u d u = sin u + C 7. ∫ sec 2 u d u = …

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Integral Table For the following, the letters a, b, n, and C represent constants. Note: Most of the following integral entries are written for indefinite integrals, but they also apply to definite …

With the exception of exponent restrictions, antiderivatives in this table appear without conditions—some are valid only when appropriate restrictions on parameters (e.g., a > 0) …

Both works contain many identities concerning specific integrals, which are organized with the most relevant topic instead of being collected into a separate table.