59 | Theorems concerning the reduction of integral formulas to the quadrature of the circle |
60 | On the resolution of an integral, if after integration the value for the determined variable quantity is assigned |
162 | A method for integrating rational differential forms involving one variable |
163 | An easier and more expedient method for integrating rational differential forms |
168 | On the controversy between Messrs Leibniz and Bernoulli concerning the logarithms of negative and imaginary numbers |
254 | On the expression of integrals as factors |
321 | Observations concerning the integrals of formulas ∫ x^{p-1}dx(1-x^{n})^{q/n-1} setting x=1 after integration |
342 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 2 |
366 | Foundations of Differential Calculus, with Applications to Finite Analysis and Series, Volume 3 |
385 | Foundations of Integral Calculus, volume 3 |
391 | On double integral formulas |
421 | Solution of a formula for the integral ∫ x^{ f-1} dx (log x)^{m/n} the integration being extended from the value x = 0 to x = 1 |
462 | On the value of the integral formula ∫ (z^{m-1} ± z^{n-m-1})/(1 ± z^{n}) dz in the case in which after integration it is put z = 1 |
463 | On the value of the integral formula ∫ (z^{λ-ω} ± z^{λ+ω})/(1 ± z^{2λ})(dz/z)(lz)^{μ} casu quo post integrationem ponitur z = 1 |
464 | A new method of determining integral qualities |
475 | Analytical speculations |
499 | On the integration of the formula ∫ (dx lx)/√(1-xx) from x = 0 to x = 1 |
500 | On the value of the integral formula ∫ ((x^{a-1} dx)/lx)(1-x^{b})(1-x^{e})/(1-x^{n}) bounded at x = 0 and extended to x = 1 |
521 | Analytical theories. Extracts of different letters of Mr. Euler to Mr. le Marquis de Condorcet |
539 | A supplement to the calculation of integrals for the calculation of irrational formulas |
572 | Nova methodus integrandi formulas differentiales rationales sine subsidio quantitatum imaginariarum |
587 | An observation on several theorems of the illustrious de la Grange |
588 | An investigation of the integral formula ∫ (x^{m-1} dx)/(1+x^{k})^{n} in the case in which after integration it is set x = ∞ |
589 | An investigation of the value of the integral ∫ (x^{m-1} dx)/(1-2x^{k}cosθ+x^{2k}) the term to be extended from x = 0 to x = ∞ |
594 | A method for finding integral formulas, for which in certain cases a given rule holds between them, where at once a method is related for summing continued fractions |
606 | Speculations concerning the integral formula ∫ (x^{n}dx)/√(aa-2bx+cxx), where at once occur exceptional observations about continued fractions |
620 | An easy method for finding the integral of the formula ∫ (dx/x)(x^{n+p} - 2x^{n}cosζ + x^{n-p})/(x^{2n} - 2x^{n}cosθ + 1) in the case in which after integration it is put from x = 1 to x = ∞ |
621 | On the greatest use of the calculus of imaginaries in analysis |
629 | The expansion of the integral formula ∫ dx(1/(1-x) + 1/(lx)) with the term extended from x = 0 to x = 1 |
630 | Uberior explicatio methodi singularis nuper expositae integralia alias maxime abscondita investigandi |
635 | Innumera theoremata circa formulas integrales, quorum demonstratio vires analyseos superare videatur |
640 | Comparatio valorum formulae integralis ∫ (x^{p-1} dx)/(^{n}√((1-x^{n})^{n-q})) a termino x = 0 usque ad x = 1 extensae |
651 | Four most noteworthy theorems on the calculation of an integral |
653 | De iterata integratione formularum integralium, dum aliquis exponens pro variabili assumitur |
656 | On most memorable integrations arising from the calculation of imaginaries |
657 | A supplement to the preceding dissertation about the integration of the formula ∫ (z^{m-1} dz)/(1-z^{n}) in the case where z = v(cos(φ) + √(-1) sin(φ)) |
662 | On the true value of the integral formula ∫ dx(l(1/x))^{n} with the term extended from x = 0 all the way to x = 1 |
668 | On the integration of the formula (dx √(1+x^{4}))/(1-x^{4}) and of others of the same type by logarithms and circular arcs |
669 | Memorabile genus formularum differentialium maxime irrationalium quas tamen ad rationalitatem perducere licet |
670 | De resolutione formulae integralis ∫ (x^{m-1} dx)(Δ + x^{n})^{λ} in seriem semper convergentem, ubi simul plura insignia artificia circa serierum summationem explicantur |
671 | De formulis differentialibus angularibus maxime irrationalibus, quas tamen per logarithmos et arcus circulares integrare licet |
672 | A memorable theorem about the integral formula ∫ (dφ cos(λφ))/(1+aa-2acos(φ))^{n+1} |
673 | A conjectural disquisition about the integral formula ∫ (dφcos(iφ))/(α+βcos(φ))^{n} |
674 | Demonstratio theorematis insignis per coniecturam eruti circa intagrationem formulae ∫ (dφ cos(iφ))/(1+aa-2acos(φ))^{n+1} |
675 | On the values of integrals where the variable term is extended x = 0 all the way to x = ∞ |
688 | A most abstruse specimen of integral contained in the formula ∫ dx/((1+x)*^{4}√(2xx-1)) |
689 | Integratio formulae differentialis maxime irrationalis, quam tamen per logarithmos et arcus circulares expedire licet |
690 | The expansion of the integral formula ∫ dz(3+zz)/((1+zz)*^{4}√(1+6zz+z^{4})) by logarithms and circular arcs |
694 | Later paper on formulas of imaginary integrals |
695 | A succinct integration of the most memorable integral formula ∫ dz/((3±zz)*^{3}√(1±3zz)) |
701 | Formae generales differentialium, quae, etsi nulla substitutione rationales reddi possunt. tamen integrationem per logarithmos et arcus circulares admittunt |
707 | On the outstanding use of the calculation of imaginations in the calculation of an integral |
721 | De integrationibus difficillimis, quarum integralia tamen aliunde exhiberi possunt |
752 | De integralibus quibusdam inventu difficillimis |
807 | On the logarithms of negative and imaginary numbers |
816 | Thoughts on certain integral formulas for which the values can be expressed under certain circumstances by the squaring of the circle |
819 | Continuation of some fragments taken from the Mathematics day book |