# Tables of Integrals and Other Math. Data by H. Dwight

By H. Dwight

By H. Dwight

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Additional resources for Tables of Integrals and Other Math. Data

Example text

B4 [ 2 x%x 1 yjF = c4 X-33abg 1x1 -y+g21. +g-gg+&]. 6. 7. 94. s x4dx 1[ -1 4a x” = @ (n - 5)XnA + (n - 4)Xn4 6a2 (n - 3)Xn3 a4 4a3 + (n - 2)Xnm2 - (n - 1)X”-’ 1 I ’ [except where any one of the exponents of X is 0, see 89]. 1. tidx s =A-2? x 4b - 4\$X + dlog 1x1 u’+~-“\$+\$log~a+bxI+const. \$i? + &2X - 4u3log 1x1 -\$I. 3. 4. 5. 6. sg=\$[-\$+&-g+-@&]. FUNCTIONS - 4ux+6a21og~x~ ++&\$I. X4dX 1 ~4 = g X - 4alog 1x1 s+g2-Lt]. [ +gL\$\$+&&]. 7. - . lOa (n - 4)X7+4 + (n 2&- g5*l. p (n -5;;x9b-2 + (n -@f)xn-i p I [except where any one of the exponents of X is 0, see891.

2. 4. 1. S S S . xdx x2==’ 1 x dx -=-. 3. 9. 2. 3. 4. 9. 1. 2 1 z3dx = - f X - \$og x2dx -=2nX”-5 xn+1 S S 1 4x2 dx x”’ S 1x1. * [n # 01. 2. 3. 9. s = ;; xSdx -p-=2x INVOLVING + ilog - 1 a2 +4x2* 1x1. 4. 2. 3. 4. 1. 2. 3. 4. 9. 1. 1. 1. dx x = 4x2 +gjp- a2 S-2dx = 2(n --1 1)x"-' +2nX" ' zs x4dx-3-a2x+%log a+x -= a--z . X I I S a2x 3a x4dx - zlog z . 1. idx s X a2x2 a4 x4 = - - - - \$og 4 2 tidx x2 x2=3+2x S ddx Sxs= S S -X””2dx S -=-x6dx X S x7dx * a2 7+4Xe 31 X = a2 - x2 Cn > 1x1. + a210g 1x1. a4 = 2(n - 12)x”-2 - ;1og 1x1.

See Fig. 140. 1 can be plotted for negative FICA 140. 01. 02. graph, l/(1 = x2 - 1 - 9:‘). 1 dz. s 1 - x2 ax s a2 - b2x2 Note that &log- a + bs = ;tanh-‘;, bx [b2x2 < a’], and &ogG bx+a 1 = actnh-f;, [b2x2 > a”]. 30 RATIONAL ALGEBRAIC &log- Note: a+x a-z &log= FUNCTIONS = i tanh-l z, [x2 < a2], = ictnh-‘E, [x2 > ae]. [Ref. 8, p. 2. 3. 4. 2. 4. 1. S S S . xdx x2==’ 1 x dx -=-. 3. 9. 2. 3. 4. 9. 1. 2 1 z3dx = - f X - \$og x2dx -=2nX”-5 xn+1 S S 1 4x2 dx x”’ S 1x1. * [n # 01. 2. 3. 9. s = ;; xSdx -p-=2x INVOLVING + ilog - 1 a2 +4x2* 1x1.