Integráltáblázatok. v du. u dv = uv. lna cosu du = sinu+c. sinu du = cosu+c. (ax+b) 1 dx = 1 a ln ax+b +C. a 2. x(ax+b) 1 dx = x a b a 2 ln ax+b +C

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József Gulyás
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1 Typote Kidó Itegráltábláztok u dv = uv v du u du = u, 1, > l cosu du = siu siu du = cosu (+b) = (+b), 1 () (+b) 1 = 1 l +b 13. () (+b) = (+b) [ +b + b ], 1, (+b) 1 = b l +b (+b) = 1 [ l +b + b ] +b (+b) = 1 b l +b ( +b) = ( +b) +, + +b = +b+b +b b = b rctg (b) b b +b +b = + +b +b +b = b b +b + = 1 rctg ( + ) = ( + ) rctg = 1 l + ( ) = ( ) l + = rsh = l (+ + ) + +b = 1 +b b l b +b+ b = + + ( ) l = 8 ( + ) + 4 ( ) 8 l + + George B. Thoms, Jr.

2 Typote Kidó 354 Itegráltábláztok = + + l + + ( ) = l ( = + l + + )+ + + = 1 l = + = rcsi = + rcsi = 4 8 rcsi 1 8 ( ) = + l = rcsi = rcsi 1 = 1 l + = = rch + = l = + l ( ) ) ( = ( ), 1 ( ) = ( ) ( ) 3 ( ) ( ), ( ) + ( ) =, + = 8 ( ) l = rcsec = l+ + = l + = 1 rcsec = 1 rccos = ( ) = rcsi George B. Thoms, Jr.

3 Typote Kidó Itegráltábláztok = + rcsi ) ( ) = ( )( ( ) ) ( )( ( = ) ( ) + 3 ( ) + ( ) ( ) = (+)( 3) ( ) rcsi ( ) = + rcsi ( ) = rcsi ( ) = rcsi = 1 si = 1 cos cos = 1 si si = si 4 cos = + si 4 si = si 1 cos cos = cos 1 si sicosb = cos(+b) (+b) sisib = coscosb = si( b) ( b) si( b) ( b) + 1 si + 1 cos cos( b), b ( b) si(+b), b (+b) + si(+b), b (+b) sicos = cos 4 si cos = si, 1 () cos si = 1 l si cos si = cos, 1 () si cos = 1 l cos si cos m = si 1 cos m (m+) m+ si cos m = si cos m 1 (m+) b+csi = b+csi = b c rctg 1 c b l + m 1 m+ [ b c ( π b+c tg 4 ) ], b > c c+bsi+ c b cos b+csi si cos m, m (visszvezethető si -re) si cos m, m (visszvezethető cos m -re), b < c George B. Thoms, Jr.

4 Typote Kidó 356 Itegráltábláztok si = 1 ( π tg 4 1 si = 1 ( π tg 4 + ) ) b+ccos = b c rctg b+ccos = 1 c b l 1+cos = 1 tg 1 cos = 1 ctg si = 1 si cos cos = 1 cos+ si [ ] b c tg, b > c b+c c+bcos+ c b si b+ccos si = cos+ 1 cos cos = si 1 si tg = 1 l sec ctg = 1 l si tg = 1 tg ctg = 1 ctg tg = tg 1 ( 1) tg, 1 ctg = ctg 1 ( 1) sec = 1 l sec+tg csc = 1 l csc+ctg sec = 1 tg csc = 1 ctg sec = sec tg ( 1) csc = csc ctg ( 1) ctg, sec tg = sec, 97. csc ctg = csc, 98. rcsi = rcsi rccos = rccos rctg = rctg 1 l(1+ ) 11. rcsi = rcsi sec, 1 csc, 1 1, 1, b < c George B. Thoms, Jr.

5 Typote Kidó Itegráltábláztok rccos = rccos+ rctg = rctg 14. e = 1 e 1, 1 1+, b = 1 b, b >, b 1 lb 16. e = e ( 1) 17. e = 1 e 1 e 18. b = b lb 1 b, b >, b 1 lb 19. e sib = e (sib bcosb) + b 11. e cosb = e + b (cosb+bsib) 111. l = l 11. (l) m = (l) m m (l) m 1, (l) m = (l)m+1, m 1 m l = l l 115. sh = 1 ch 116. ch = 1 sh sh = sh 4 ch = sh 4 + sh = sh 1 ch ch = ch 1 sh sh = ch 1 sh 1. ch = sh 1 ch 13. sh = ch 1 ch 14. ch = sh 1 sh 15. th = 1 l(ch) 16. cth = 1 l sh 17. th = 1 th 18. cth = 1 cth th = th 1 ( 1) + cth = cth 1 ( 1) + th, 1 sh, ch, cth, 1 George B. Thoms, Jr.

6 Typote Kidó 358 Itegráltábláztok 131. sech = 1 rcsi(th) 13. csch = 1 l th 133. sech = 1 th 134. csch = 1 cth sech = sech th ( 1) csch = csch cth ( 1) sech th = sech, csch cth = csch, e shb = e e chb = e [ e b +b e b b [ e b +b + e b b e = Γ() = ( 1)!, > 14. e = 1 π, > 143. π/ si = sech, 1 ], b ], b csch, 1 π/ ( 1) π, h páros egész szám cos = ( 1), h 3 pártl egész szám George B. Thoms, Jr.

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