Page 184 - Demo

178 Përgjigjet b i 1 1 sin 42 8x xc   ii 1 1 sin 48 2x xc  2 a 1 cos22 x cb 1 cos2 2cos2  x xc c 1 sin 22x c 3 d i 1 2 2 ( 5)2xx c   ii 1 2 (sin )2 x c iii 1 2 (ln )2 x c iv 1 2 2 ( 1)2x e c  f i ln sin x c ii ln( 3) x e c   iii ln ln x c 4 d i 1 4ln 4x  c ii 1 2 52ln5x  c iii 1 1 3ln 3x c  Ushtrime 5.3A1 a 3xsin x+3cos x+c b 2xcos x+2sin x+cf 1 sin(1 4 ) cos(1 4 ) 20 80x − −+ −+ x xc g (2x+3)cos x+2sin x+c2 a 3xex3ex+c d1 1 2 2 ( 2)2 4x x x e ec  e 1 5 12 12 (3 5 )2 4x x xe e c    f 1 1 13 13 (3 2)3 3x x xe e c      3 a 22 ln2xxx c  b 5 5 2 2 ln2 4x x xc   c 2 2ln2 4x x x x xc § ·§ ·    ¨ ¸¨ ¸ © ¹© ¹d 22 ( )ln 2 2x xx x xc § ·    ¨ ¸ © ¹e 2 ln 2 4 x x xc  f 52 25x c 4 a 1 b 109c d45  ln55 e 5  10e1f 05 a 0sin0 = SsinS= 2Ssin2S= 0 b i S ii 3S c 4SUshtrime 5.3B1 a xln4xx+c b 1 ln(3 1) ln 3 1 3xx x x c   c1 3 83 8 ln( ) 8 64x x xc  de x lnx+x+c f 2 x x xxx c (ln ) 2( ln )  2 a 2 2 2 x xx x e xe e c  b 2 x x x x xc sin 2 cos 2sin + −+c 2 (1 3 ) 6(1 3 ) 18 x xx     x e xe e c d 11 1 2 8 9 10 ( 1) ( 1) ( 1) 8 36 360x x xx x c +− ++ + +e f 111 26 7 8 ( 1) ( 3) ( 1)( 3) ( 3)6 21 168 x x xx x c + +− + ++ ++g1 11 2 cos2 sin 2 cos22 24   x x x x xch 122 2 sin 3 cos3 sin 33 9 27x x x x xc  3 a13 54 69 e  b 2 132 4S  c 2S4 a x2ex2xex+2ex+cb y= x2ex2xex+2ex=ex(x22x+2)