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### Contents

 I 3 II 5 III 16 IV 31
 V 35 VI 62 VII 66 Copyright

### Popular passages

Page 15 - If any of the roots of the equation f(x) = 0 are imaginary, the parts of the integral which arise from conjugate roots can be combined together and the integral brought into a real form.
Page 77 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 14 - The simpler fractions, into which the original fraction is thus divided, may be integrated by means of the following formulas : � hdx _ rhd(mx + n) h " ' )' Jm(mx + n)1 m(l — l)(mx + n)l~l 72.
Page 23 - X A +Bx — я? = 0, if с < 0 and — < 0. — с By rationalization, or by the aid of reduction formulas, may be obtained the values of the following integrals : 120 121. 20. f _^L = -^log(Vx + x Vc + -V), if с > 0. J VX V^ V 2^cJ VA
Page 60 - ... /sinh x cos x dx = � (cosh x cos x + sinh x sin x). 21. fe? sin x cos xdx = ^ (sin 2x - 2 cos 2x) e*. 22. /xV <& = - (x4 + Sx4 + 20x" + GOx
Page 124 - The Common Logarithms of T(n) for Values of n between 1 and 2...
Page 107 - ... represent the angles between n and the directions in which and rj, respectively, increase most rapidly・ 880・ 汀汀 れ・礼・刀。