Handbook of Mathematical Formulas and Integrals (4th by Alan Jeffrey, Hui Hui Dai

By Alan Jeffrey, Hui Hui Dai

The huge additions, and the inclusion of a brand new bankruptcy, has made this vintage paintings by way of Jeffrey, now joined by way of co-author Dr. H.H. Dai, an excellent extra crucial reference for researchers and scholars in utilized arithmetic, engineering, and physics. It presents easy accessibility to big formulation, relationships among services, and mathematical concepts that variety from matrix concept and integrals of more often than not happening services to vector calculus, usual and partial differential equations, detailed services, Fourier sequence, orthogonal polynomials, and Laplace and Fourier transforms. throughout the training of this variation complete virtue used to be taken of the lately up-to-date 7th version of Gradshteyn and Ryzhik's desk of Integrals, sequence, and items and different very important reference works. feedback from clients of the 3rd version of the guide have led to the growth of many sections, and thanks to the relevance to boundary price difficulties for the Laplace equation within the airplane, a brand new bankruptcy on conformal mapping, has been additional, whole with an atlas of priceless mappings. a special function of the fourth variation is the supply of a CD-ROM that gives prepared entry to the main often used components of the publication, including worthy notes for clients of the guide.

- accomplished assurance in reference kind of the branches of arithmetic utilized in technology and engineering<BR id="CRLF">- equipped to make effects related to integrals and capabilities effortless to locate<BR id="CRLF">- effects illustrated through labored examples <BR id="CRLF">- targeted CD-ROM that presents entry to the main usually used components of the book<BR id="CRLF">- CD-ROM includes precious notes for clients

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87. 88. 89. 90. 91. 92. 93. 94. sinh 2ax x + 4a 2 x 1 x cosh ax dx = sinh ax − 2 cosh ax a a eax ebx e−bx eax sinh bx dx = − 2 a+b a−b ax bx e e e−bx eax cosh bx dx = + 2 a+b a−b 1 2ax 1 ax e sinh ax dx = − x e 4a 2 1 1 e2ax + x eax cosh ax dx = 4a 2 1 tanh ax dx = ln (cosh ax) a 1 tanh2 ax dx = x − tanh ax a 1 coth ax dx = ln |sinh ax| a 1 coth2 ax dx = x − coth ax a 2 arctan eax sech ax dx = a 1 sech2 ax dx = tanh ax a 1 ax csch ax dx = ln tanh a 2 1 csch2 ax dx = − coth ax a 9 cosh2 ax dx = [a2 = b2 ] [a2 = b2 ] Integrands involving inverse hyperbolic functions 95.

2 (2a + c) Formed by four equilateral triangles. √ Surface area A = a2 3. √ a3 2 Volume V = . 12 2 4h2 + 4 (a − c) . 8 Geometry 17 The centroid C is located on the line from the centroid O of the base triangle to the vertex, with OC = h/4. Oblique prism with plane end faces If AB is the area of a plane end face and h is the perpendicular distance between the parallel end faces, then Total area = Area of plane sides + 2AB . Volume V = AB h. The centroid C is located at the midpoint of the line C1 C2 joining the centroid of the parallel end faces.

5 1 ln |cosh ax| a x 1 √ dx = arcsin [x2 ≤ a2 ] a a2 − x2 x 1 √ dx = arccosh = ln |x + x2 − a2 | [a2 ≤ x2 ] 2 2 a x −a x 1 √ dx = arcsinh = ln |x + a2 + x2 | a a2 − x2 1 1 x dx = arctan x2 + a2 a a 1 dx a + bx 1 bx = ln = arctanh [a2 > b2 x2 ] 2 2 2 a −b x 2 ab a − bx ab a tanh ax dx = Integrands involving algebraic functions (a + bx)n + 1 b(n + 1) 17. (a + bx)n dx = 18. 1 1 dx = ln |a + bx| a + bx b 19. x(a + bx)n dx = 20. [n = −1] (a + bx)n + 1 a + bx a − b2 n+2 n+1 x x a dx = − 2 ln |a + bx| a + bx b b [n = −1, −2] 21.

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