333 TICH PHAN HAY

333 BÀI TỐN TÍCH PHÂN LUYỆN THI ĐẠI HỌC 1/ Cho hàm số : f(x)= x.sinx+x2 Tìm nguyên hàm hàm số g(x)= x.cosx biết nguyên hàm triệt tiêu x=k  2/Định m để hàm số: F(x) = mx +(3m+2)x2 -4x+3 nguyên hàm hàm số: f(x) = 3x2 +10x-4 3/Tìm họ nguyên hàm hàm số: f(x)= cos x.sin8x TÍNH :  3tg x dx 4/I = �   94/I = 6/I = �  cos x e2 7/ I = e 96/I = dx 97/I = �x  2x  x  dx  sin x.cos xdx 1 3 8/I = 2  (2cos x-3sin x)dx   x) dx 9/ I= �   sin(   x)  2 �x  dx 4 2  sin( 98/I = � cos 2x  1dx   cos x 99/I = �   (tgx-cotgx)  11/ I = cos x dx � 12 / I =  sin x dx � dx sin xdx 2 100/I = �1  sin xdx 3  10 / I = 1  )dx ln x ln x 95*/I = � (  cos x dx �  5sin x  sin x (2cotg x  5) dx 5/I = �    cos x  101/I = �sin 2x dx   102/I = �1  sin xdx � ln(x  x  1) � 103/I = � � �dx 1  x sin x dx  cos x 104*/I = �  3 sin x  sin x cot gx dx 13*/ I = � sin x   14/I = sin x dx � dx x (x  1)(4  1) 1 x4 106*/I = � x dx 1  105*/I = � 107/I =  dx  x x  sin cos 2 15/I = 2 �x sin xdx 108/I = 2 �x cos xdx  16/I =  cotg2x dx   esin 17/I = � x sin 2x dx  18/  e tgx 2  cos x I=  19/ I =  dx  sin x 128*/I =   dx  cos x  21/I = cos x( sin x  cos x )dx  22/ I = cos3 xdx � 23/ I =  24/ I = 4sin x dx �  cosx x  x dx � sin 2x �(2  sin x) dx 20/ I = dx x  4x  5 dx 124/I = �2 x  6x  1 dx 125/I = � 2x  8x  26 5 2x  dx 126/I = � x  dx 127/I = �2 x (x  1) 123/I = �2 x 3 dx (x  1)(x  3x  2) 4x dx 130/I = � (x  1) 1 dx 131/I = � (x  4x  3) 129/I = � 132/I =  sin x dx � (sin x  3)  4sin x dx 133/I = �  cos x   x  x dx 25/I = � x dx 2x  1 dx 27/I = �x 0e 4 28/I = �  x dx 11 e e 2x dx 29/I = �x e  1 e x dx 30/I = � x e  e ln x dx 31/I = � x(ln x  1) 1 dx cos x.sin x  134/I = � 26/I = � 32/I = 135/I = sin x.tgxdx �  136/I = x 1 dx 3x  34/I = 152/I = 153/I = 35/I = � 36*/I = x 16  x � 37/I = 155/I = 4x �x dx dx x x 9 dx  x dx 1 x (x  4)3 dx 38/I = � 39/I = � 3  40*/I = 2 ln 41/I = x2  dx x x2 1 x � e  1dx � 1 e 2x x 9x dx dx  cos x dx � 4 cos x  sin x 156/I = �  dx x9  x x sin xdx 157/I = �  x cos xdx 158/I = � cos x dx 159/I = � sin x dx 160/I = � 161/I = dx x x 1 � � 3e4x  e 2x 154/I = e x sin xdx � x �2  (x  3) x  6x  dx 33/I = � 1 dx � sin 2x  �3  2 �x sin x dx 162/I =  �x cos x dx  1 dx 42/I = �  2x x cos x sin x dx 163/I = �  43/I = sin xdx � 164/I = e x dx 165/I = � 44*/I = dx � cos x  e 2x dx 45/I = � x e  ln dx 46/I = � x e 1 47/I = �  166/I = e3x sin 4x dx � dx ln x  ln x 48/I = � dx x e e sin(ln x) dx x 49/I = � x (x  1)5 dx 50/I = � (1  2x)(1  3x  3x )3 dx 51/I = � 52/I = � 1x  1 x dx 189/I = � 54/I = �(1  x ) dx 1 dx 55*/I = �2x e  ln ex 15  x dx x 188/I = � x (e  1) ex  � 1 2 53/I = �tg x  cot g x  2dx 56/I =  sin 2x dx �  cos x dx 183/I = �2 x  6x  x  3x  dx 184/I = � x  dx 185/I = �2 x (x  1) 1 ln(1  x) dx 186/I = � x  1 1 x4 187/I � dx 01 x 182/I = sin x cot gx x cos x sin x dx �    e 190/I= x e e x dx ln x dx � e  191/I = (esin x  cos x) cos x dx �  192/I = sin 2x.cos x dx dx �1  cos x 0 x(e 57/I = � 58/I 2x  x  1)dx 1  = �1  cos x sin x.cos xdx � 59*/I = 60/I =  x x 4 dx e 2x dx ln e  e x 1 ln xdx 62/I = � x 61/I = � 193/I = sin 2x  sin x dx � 194/I = x x2 dx 63/I = � (x  1) x  1   x7 dx 67/I = �  x  2x  68*/I = 4cos x  3sin x  dx � 4sin x  3cos x  x  xdx 69/I = � x 1 dx 3x   x sin dx 71*/I = � 2 x dx 72*/I = �  x   x tgx dx x2 212/I = � dx 4x x 213/I = � dx 4x x 1 dx cos x  cos x  65/I = cos 2x(sin x  cos x)dx � 66*/I = ( cos x  sin x )dx � 196/I = � 215/I =  x  2x � 195/I = 64/I = sin x.sin 2x.sin 3xdx � 70/I = � �1  sin 2x dx 214/I =  2  3cos x   2sin x x dx �  cos 2x ln  216/I = x4 dx � x   sin 3x dx � cos x  2 � x2 1 x 1 x2 217/I = � dx 11 x 218/I = �3 x3 dx dx 1 x  ex 219/I = � x dx 1 e ln x  x dx 220/I = � 221/I = �x  1dx  222/I = (cos3 x  sin x) dx � 73/I = �x  x dx ln(1  x) dx 74**/I = � x 1 75/I =  sin x dx � sin x  cos x x2  dx 223/I = � x  (1  x) e2x dx 224/I = � 225/I = e  cos(ln x)dx 76/I = � 226/I =  � 77*/I = �4  x dx cos x  dx x 1 dx 3x  �3 cos x  x dx 78/I = � 1  x 1 242/I = sin 2x  sin x dx  3ln x ln x dx 79/I = � x 243/I = e � ln(x  x)dx 80/I = � 244/I = (ln x) dx 81/I = � 245/I = e2 ln x dx 82/I = � x e ln x dx ln x x ln(x  1)dx 84/I = � dx 85/I = � x  3 1 dx 86/I = � 4x 87/I = 2 2 � �sin xdx 2 � x3 1 x x3 1 x dx dx 1 x2 246/I = � x dx 2 83/I = � sin 2x dx � 2 sin x  2cos x 0 e e2 cos3x   x2 247/I = � 248/I = 4x � 2 dx x x 1 dx x (1  x )6 dx 249/I = � 250/I = 251/I =  sin x dx �  sin x  � cos x dx  cos 2x  ln(sin x) 88/I = � dx  cos x cos(ln x)dx 89/I = � ln(  x  x)dx 90*/I = � � 91*/I = x 1 x 1 dx 92/I = � x x3 dx 93/I = �2 x  16 dx  109/I = x.sin x cos xdx �  cos x  sin x dx  sin 2x  254*/I = � 267/I = x e dx (x  2) 110*/I = � 2x 268/I = e ln x dx � 113/I = (x  1) e 4 270/I = sin x  cos x dx � 0 1 x t �ln x � 115/I = � � �dx � I  �x �  116/I = sin x.ln(cos x)dx �  117/I = e2 �cos (ln x)dx sin x  cos x   4 271/I = sin x  cos x dx �  sin x  cos x  272/I = sin x cos x  cos x dx � sin x  273/I = 114/I = x.ln  x dx � sin x dx � x 0  x 2 269/I = sin x cos x(1  cos x) dx � e sin xdx 111/I = � x ln(1  )dx 112/I = � sin x dx � cos x   2  2 x  dx (1  x)x x 1 dx 253/I = � 3x  252/I = � 1 ex dx � x3 a x  2x  10x  dx 274/I = � x  2x  x3 dx 275/I = � (x  1) dx 276/I = �3 x 1 x 1 dx 277*/I = �6 x 1  x dx (2x  1) dx 279/I = �  x  278/I = � 118/I = dx � cos x 119*/I =  dx � cos3 x 280/I = x2 x e dx 120/I = � 137/I = 295/I = sin 2x dx �  cos x  296/I = sin x dx � (tg x  1) cos5 x 1 301/I = dx � x (x  1) 1 302/I = dx 303/I =  304/I = x  xdx 145/I = � dx  1 x dx dx  sin x cos x cos x 144/I = sin x dx � cos x dx 300/I = � dx � sin x  cos x  x   (x  4)   sin x � dx dx  1 x 1  x dx �  3cos x 3 1 x x 1 x x3 299/I = � 143/I = �3 0x    x3 297*/I = �  142/I = x x 1 cos x  dx 139/I = � cos x   141/I = 298/I = �  140/I = � �sin x  9cos x dx  2  138/I = x 1 x dx 121/I = esin x sin x cos xdx � 122/I = �   305/I =  cos x dx � cos x   cos x dx �  cos x  sin x dx � sin x   cos3 x dx � cos x   dx � 2cos x  sin x  x4 dx x  x  dx 147/I = � 1 x  2x  dx 148/I = � 4x  x 146/I = �  2 � 4x  x  dx 1 2x  � 150/I = 307/I = tg x dx � x  4x  13 dx 151/I = � x 3e  321*/I = tg x dx � dx 2  cotg x dx 322/I = �    e 2x sin x dx 167/I = � x 2e x dx 168/I = � (x  2) e (1  x) ln x dx 169/I = � e x ln x dx 170/I = � 1 e 323/I = e2 1 (  )dx 173/I = � ln x e ln x (x  x) ln x dx 174/I = � x x ln(1  ) dx 175/I = � ln x x e ln x dx 177/I = 1� (x  1) e dx �  tgx 325/I =  sin x dx � cos x  cos 2x dx   cos 2x 176/I = � dx  324*/I = x(2  ln x) dx 172/I = �  326/I = � e tg x dx �  171/I = ln x dx �   149/I = cos x dx � (1  cos x) 306/I =  327*/I = ( t gx  1) dx � tgx  1 x 328*/I = � x  1dx 2 x  x3 329*/I = � dx x ln ex 330/I = � x x (e  1) e  dx  178/I = x ln  x dx � 1 x  cos x.ln(1  cos x) dx 179/I = �  180/ esin x sin x cos3 x dx �  sin 2x dx �  sin x x 1 ) dx x2 ( 197/I = � 1  198/I = x.tg x dx � ( x   x  )dx 199/I = � 3 dx 1 x   x dx 201/I = � x    x 200/I = � ln(1  x) dx x 202/I = � 203/I = 204/I = 331/I = 1  sin 2x dx �  cos x  sin 2008 x dx � 2008 2008 sin x  cos x  205/I = sin x.ln(1  cos x) dx � x2 1 206/I = � dx x �x cos (ln x  1) dx e  333*/I = ln(1  tgx)dx �  181/I= e4  207/I = sin x dx �  cos x 208/I = cos x.cos 4x dx � 1 dx x e  e e ln x dx 210/I = 1� (x  1) 209/I = �2x e 211/I = � dx x 1  x   sin 2x 227/I = �   cos 2x dx cos x  sin x (1  e x ) 228/I = � 2x dx 1 e x (1  x)3 dx 229/I = � 230/I = 231/I =  sin x.cos3 x �cos x  dx 4x  dx � x  3x   x sin x.cos xdx 232*/I = �  cos x dx cos 2x  dx 234/I = �2 x (x  1) 233/I = �  235/I = sin 2x(1  sin x)3 dx � x 1 dx 3x  236/I = � 237/I = �  x x 9 dx x sin x cos xdx 238/I = �  239/I = �cos x cos x  cos xdx   ln( x  a  x)dx 240*/I = � 241/I =  1  sin x dx � x (1  cos x)e  255/I = �cos x cos x  cos xdx    tg xdx 256/I = �  257*/I =   sin x e x dx �  cos x 258/I = �(1  x ) dx  259/I = x.tg xdx � dx 2 (4  x ) 3x dx 261/I = � x 2  x5 dx 262*/I = � x(1  x ) 260/I= � 263/I =  cos x dx �  sin x  264/I = sin x dx � cos x  265/I = sin x  sin x dx � cos 2x  dx sin x  cos x  265/I = � 3 266/I = �x (1  x ) dx x ln(x   x ) 281*/I = � 1 x dx (x  1) ln x dx 282/I = � x ln(x  1) dx 283/I = � 3x dx 284/I = �2 x  2x  1 4x  dx 285/I = �3 x  2x  x  2 286/I = 1 (3  2x) 287/I = � 288/I = �   12x  4x x  1 x dx cos x dx �  cos 2x  cos x  sin x dx  sin 2x  289/I = �  290/I = (cos3 x  sin x)dx � dx  291/I = cos5 x sin xdx �  292/I = cos 2x(sin x  cos x)dx � 293/I = 294/I =  dx �  sin x  dx �  cos x 1 dx 2x  e 1  sin x dx 309*/I = � x   308*/I = � 310*/I =  sin x dx � cos x  sin x 311/I =  sin x dx � 4 cos x  sin x  tgx 312*/I = �  ln (cos x) dx  sin x dx cos x  sin x 1 dx 314*/I = � x (e  1)(x  1) 1 313*/I = � e 315*/I = � 316*/I = � 317*/I =  3x 1 dx x2 x 4 dx cos3 x dx � cos  3cos x  t 2et dt  318*/Tìm x> cho � (t  2) x  319*/I = �  tan x cos x cos x  dx 320*/I = �3x  6x  1dx  ... sin x  cos x  205/I = sin x.ln(1  cos x) dx � x2 1 206/I = � dx x �x cos (ln x  1) dx e  333* /I = ln(1  tgx)dx �  181/I= e4  207/I = sin x dx �  cos x 208/I = cos x.cos 4x dx � 1 dx