| Ⅰ Introduction Ⅱ Elementary functions and their classification Ⅲ The integration of elementary functions Summary of results Ⅳ The integration of rational functions 1-3 The method of partial fractions 4 Hermite's method of integration 5 Particular problems of integration 6 The limitations of the methods of integration 7 Conclusion Ⅴ The integration of algebraical functions 1 Algebraical funef, ions 2 Integration by rationalisation Integrals associated withconics 3-6 The integral fR {x, √(ax2 +2bx + c)} dx 7 Unieursal plane curves 8 Particular cases 9 Unicursal curves in space 10 Integrals of algebraical functions in general 11-14 The general form of the integral of an algebraical function. Integrals which are themselves algebraical 15 Discussion of a particular case 16 The transcendence of ex and log x 17 Laplace's principle 18 The general form of the integral of an algebraical function(contegred). Integrals expressible by algebraieaI functions and logarithms 19 Elliptic and pseudo-elliptic integrals Binomial integrals 20 Curves of deficiency 1 The plane cubic 21 Degenerate Abelian integrals 22 The classification of elliptic integrals Ⅵ The integration of transcendental functions 1 Preliminary 2 The integral f R (eax ebx, …, ekx) dx 3 The integral f P ( x, eax ebx…) dx 4 The integral f ex R (x) dx The logarithm-integral 5 Liouville's general theorem 6 The integral f log x R (x) dx 7 Conclusion Appendix Ⅰ Bibliegraphy Appendix Ⅱ On Abel's proof of the theorem of v., 11 |
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