[PDF] Top 20 Solving Real Integrals Using Complex Integrals

... In calculus and engineering mathematics, there are many methods to solve the integral problems, including change of variables method, integration by parts method, partial fractions method, trigonometric substitution ... See full document

... This paper uses the mathematical software Maple for the auxiliary tool to study two types of integral problems of trigonometric functions. We can obtain the closed forms of the two types of integrals using ... See full document

... are real numbers for all k = 1 ...multiple integrals by using binomial series and integration term by term theorem; these are the major results of this study ...multiple integrals to do ... See full document

... are real numbers, and b ≠ 0 ...of integrals by using binomial series and integration term by term theorem ; these are the major results of this study ... See full document

... For the definite integral problems discussed in this study, two examples are provided and we use Theorems 1 and 2 to obtain their infinite series expressions. Moreover, Maple is used to calculate the approximations of ... See full document

... In the next part we define some global functions. The function MakeComb takes the integer arguments n and k and gives a list of all subsets of {1,...,n} with length k. The functions GetBasis, RepMom and ruleI are well ... See full document

... To establish the theorem 1, expressing the multivariable Gimel-function in the Mellin-Barnes multiple integrals contour with the help of (1.1) and interchanging the order of integrations which is justified under ... See full document

... The rest of this paper is organized as follows. After recalling some notation and estab- lishing some preliminary lemmas, we will prove Theorem . in Section . And the proof of Theorem . will be given in Section . ... See full document

... obtained using a range of ab initio methods (Hartree-Fock, second-order Moller-Plesset perturbation theory (MP2), orbital-optimized coupled-cluster theory with double excitations (OO-CCD) and coupled-cluster ... See full document

... In this paper, we establish a new Hermite–Hadamard inequality involving left-sided and right-sided ψ -Riemann–Liouville fractional integrals via convex functions. We also show two basic ψ -Riemann–Liouville ... See full document

... given for the elementary functions of n-complex variables. The exponential function of an n-complex number is expanded in terms of functions called in this paper n- dimensional cosexponential functions of ... See full document

... t using only addition, multiplication, and (possibly iterated) integration with respect to B and t, which we shall call “polynomial ...classical integrals alone (no Itô integrals) by repeated ... See full document

... In this paper, we use Laplace transform to solve some improper integrals. In fact, the applications of Laplace transform are extensive, and can be used to easily solve many difficult problems; we endeavor to ... See full document

... Abstract. Using some inequalities for real numbers and integrals we point out here some new inequalities for the moments of guessing mapping which generalize and improve the recent results of Arikan ... See full document

... The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C + (x), C − (x), S + (x), and S − (x) are defined as locally summable func- tions on the real line. Some convolutions ... See full document

... Remark 3.14 An important application of integrals in finite dimension Hopf algebra is Maschke theorem. It finds the condition of finite dimension Hopf algebras to be semisimple. [12-14] have studied the relation ... See full document

... several interpretations are given by means of multiplicative derivatives where the logarithmic scale appears. Actually, many of the scientific tables are given in logarithmic scales. For ex- ample, the level of sound ... See full document

... parts using the (shortcut) or tabular integration makes integration clear, neat, and ...parts using the traditional method is considered to be long, misleading, and sometimes hard for average and good ... See full document

... In calculus and engineering mathematics courses, we learnt many methods to solve the integral problems, including change of variables method, integration by parts method, partial fractions method, trigonometric ... See full document

... In [13], Skoug and Yoo expressed the analytic Wiener and Feynman integrals as the limits of Wiener integrals, and then they established a change of scale formula for Wiener integrals on [r] ... See full document