Tables of Indefinite Integrals

Integration by Tables is possible if an integral may be put into a form that can be found in a table of integrals, such as the one given in Table 1-7. More complete tables may be found in Bois, Tables of Indefinite Integrals, Dover, and in others. 

It follows that the functions in the left-hand column of the preceding table are the integrals of the functions in the right-hand column. More formally, they are the indefinite integrals of the function, in contrast to the definite integrals described next. Tables of indefinite integrals in reference books may be consulted for more complex examples, or mathematical software can be used to evaluate them. 

Ozisik, M.N. 1968. Boundary value problems of heat conduction. Int. Textbook Co., Scranton, PA. Petit Bois, G. 1961. Tables of indefinite integrals. Dover Publ. Inc., New York. 

This integral is called an indefinite integral, since the lower limit is unspecified and the upper limit is variable. The indefinite integral is the same as the antiderivative function. Large tables of indefinite integrals have been compiled. Appendix E is a brief version of such a table. In most such tables, the notation of Eq. (5.33) is not maintained. The entries are written in the form... 

The same information is contained in a table of indefinite integrals as is contained in a table of derivatives. However, we can get by with a fairly short table of derivatives, since we have the chain rule and other facts listed in Section 4.4. Antiderivatives are harder to find, so it is good to have a separate table of indefinite integrals, arranged so that similar integrand functions occur together. 

SOLUTION From Appendix E or any published table of indefinite integrals,... 

EXAMPLE 5.8 Using a table of indefinite integrals, find the definite integral... 

C) Substitute your expression for [5] into the mass balance and solve for [A]. Your expression for [A] should contain only kf, kh, [A]o, and t. (You may wish to consult the table of indefinite integrals in Appendix E.)... 

Formally the solution can be found by noting that the right hand side is simply -kt and by finding (e.g. in a table of indefinite integrals) that the... 

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