333 bài toán tích phân luyện thi đại học26235

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 :  4/I =  3tg x dx        cos x   cos x dx  13*/ I = 5/I =  (2cotg x  5) dx 6/I =  sin x dx 12 / I =  sin x  sin x cot gx dx sin x   sin x dx 14/I =   x x dx sin cos 2   15/I = 7/ I =  sin2 x.cos2xdx   8/I =  (2cos2 x-3sin2 x)dx 9/ I=      x) dx  sin(  x) 4 16/I =   cotg2x dx sin(  17/I =  esin  sin 2x dx   x   10 / I = 18/  11/ I =  cos x dx e tgx  2 I=  cos x (tgx-cotgx)2 dx 34/I =  ThuVienDeThi.com x 4x dx  35/I =  19/ I =  sin x dx  36*/I =   cos x 37/I =  4sin x 23/ I =  dx  cosx  x  x dx 24/ I = 25/I =  x 3   x dx x dx 2x  1 27/I =  x dx 0e 4 28/I =  dx x 11 e e 2x 29/I =  x dx e 1 e x 30/I =   x dx 1 0e e ln x 31/I =  dx x(ln x  1) 26/I =  32/I =  x 1 dx 3x   40*/I = 2 ln 41/I = x2 1 dx x x 1 x  e  1dx 42/I =   x2  dx x  39/I = dx 2  x  x dx 22/ I =  cos xdx x x 9 38/I =  x (x  4)3 dx dx 1 4  cos x(sin x  cos x)dx   2 dx  21/I = x 16  x 20/ I = 1 dx  2x 43/I =  sin xdx  dx cos x 44*/I =  e 2x 45/I =   x dx e  ln dx 46/I =  x e 1  47/I =   sin x cot gx dx ln x  ln x 48/I =  dx x e 33/I =  (x  3) x  6x  dx ThuVienDeThi.com  e sin(ln x) dx x 64/I =  sin x.sin 2x.sin 3xdx 49/I =   50/I =  x (x  1)5 dx 65/I =  cos 2x(sin x  cos x)dx 51/I =  (1  2x)(1  3x  3x ) dx  2 66*/I =  ( cos x  sin x )dx 52/I =  1 x 1x  3 dx x7 67/I =  dx  x  2x 53/I =  tg x  cot g x  2dx  4cos x  3sin x  dx 4sin x  3cos x   68*/I =  54/I =  (1  x )3 dx 69/I =  x  xdx 1 55*/I =  2x dx e  ln ex 56/I =  (e  1) x x 1 dx 3x   x 71*/I =  sin dx 2 x 72*/I =  dx  x   x 70/I =  dx 57/I =  x(e 2x  x  1)dx 1  58/I =   cos x sin x.cos xdx 73/I = 0  x x 4 dx  x 60/I =  dx  cos 2x ln  e 2x dx x ln e  e x 1 62/I =  ln xdx x 61/I = x2 63/I =  dx (x  1) x  1 ln(1  x) dx x  1 59*/I =  x  x dx 74**/I =   sin x dx sin x  cos x 75/I =  e 76/I =  cos(ln x)dx 77*/I =   x dx x dx  x  1 78/I =  ThuVienDeThi.com  3ln x ln x dx x e 79/I =  80/I =  ln(x  x)dx  cos x dx  5sin x  sin x 94/I =  e2 95*/I =  ( e e 81/I =  (ln x) dx 96/I = 97/I =  x  2x  x  dx ln x dx x 82/I =  e e2 1 3 ln x dx ln x 83/I =  98/I = 84/I =  x ln(x  1)dx 85/I = 1 4x 86/I =    99/I =  cos x sin xdx 2 100/I =   sin xdx 3 dx  sin 2x dx  101/I =  ln(sin x) 102/I =   sin xdx 87/I =  cos 2x  1dx  x  dx  x  dx 4 e 1  )dx ln x ln x    sin xdx 88/I =  cos x  dx 90*/I =  ln(  x  x)dx  x 1 x 1 92/I =  dx x x3 93/I =  dx x  16 dx 103/I =   ln(x  x  1)  dx   1  89/I =  cos(ln x)dx 91*/I = x sin x dx  cos x 1 105*/I =  dx x 1 (x  1)(4  1) x4 106*/I =  dx x 1  104*/I =  2 107/I =  x sin xdx 2 108/I =  x cos xdx ThuVienDeThi.com  109/I =  x.sin x cos xdx x 2ex 110*/I =  dx (x  2)  111/I =  e 2x sin xdx x 112/I =  x ln(1  )dx dx x  4x  5 124/I =  dx x  6x  1 125/I =  dx 2x  8x  26 5 2x  126/I =  dx x  127/I =  dx x (x  1) 123/I =  e ln x dx (x  1) 113/I =  e 128*/I = 114/I =  x.ln 1 x dx 1 x 129/I =   116/I =  sin x.ln(cos x)dx  sin x dx 132/I =  (sin x  3)  e2  cos (ln x)dx   4sin x dx 133/I =    cos x dx cos x 118/I =    dx cos x.sin x  dx cos x 134/I =  119*/I =  x 3 dx (x  1)(x  3x  2) 4x 130/I =  dx (x  1) 1 131/I =  dx (x  4x  3)  ln x  115/I =    dx  I  x   t 117/I =  3 x2 120/I =  x e dx  121/I =  e  sin 2x dx   (2  sin x) 135/I =  sin x.tgxdx sin x  3 sin x cos xdx sin 2x 122/I =  dx  cos x 136/I =  ThuVienDeThi.com  sin 2x dx  sin x 137/I =  dx 2 (tg x  1) cos x  138/I = 152/I = 139/I = 140/I = cos x  1  sin x 156/I =   cos x dx 141/I =  sin x  cos x  142/I =  dx x (x  1) 1 3 x   (x  4)  sin x dx 144/I =  cos x 0  158/I =  x cos xdx dx 159/I =  cos x dx 160/I =  sin x dx 2 145/I =  x  xdx 146/I =   147/I = 1 148/I =  1 x4 dx x2 x2 dx x  2x  dx 4x  x  150/I = 2 151/I =  2x  x  4x  13 dx x 3 e  x sin x dx 161/I =  4x  x  dx 149/I = dx x 9  x 157/I =  x sin xdx dx cos x 155/I =  dx 4 cos x  sin x   3cos x dx  x 9x dx   143/I = 2x 154/I =  e x sin xdx  cos x  dx        1 e 153/I =  sin x  9cos x dx   3e 4x  e 2x dx  162/I =  x cos x dx  163/I =  x cos x sin x dx  164/I =  x cos x sin x dx 165/I =  e  x dx 166/I =  e3x sin 4x dx ThuVienDeThi.com  167/I =  e 2x sin x dx x 2ex 168/I =  dx (x  2) e 169/I =  (1  x) ln x dx e 170/I =  x ln x dx 1 e 171/I =  ln x dx e 172/I =  x(2  ln x) dx e2 1 )dx 173/I =  (  ln x e ln x  sin 2x dx  cos x 183/I =  dx x  6x  1 x  3x  184/I =  dx x  185/I =  dx x (x  1) ln(1  x) 186/I =  dx x  1 1 x4 187/I  dx  x 182/I =  188/I =  x15  x dx 174/I =  (x  x) ln x dx x 175/I =  x ln(1  ) dx ln x 176/I =  dx x e ln x 177/I =  dx (x  1) e 178/I =  x ln  1 x dx 1 x 189/I =  190/I= e  191/I =  (esin x  cos x) cos x dx  sin 2x.cos x dx  cos x 192/I =   sin 2x  sin x dx  3cos x   2sin x dx  sin 2x 194/I =  x sin x cos3 x dx   195/I = sin 2x   sin x dx dx  ln x dx 180/  esin x 193/I =   181/I= e e x e 179/I =  cos x.ln(1  cos x) dx  ex  196/I =   ThuVienDeThi.com x  2x x 1 dx tgx cos x  cos x dx x 1 197/I =  ( ) dx x  1  198/I =  x.tg x dx 199/I =  ( x   x  ) dx 3 dx 1 x   x 201/I =  dx x    x 200/I =  x2 212/I =  dx  x x 213/I =  dx  x 1 x4 214/I =  dx x   sin 3x dx cos x  215/I =  2 216/I = ln(1  x) 202/I =  dx x  sin 2x dx  cos x sin 2008 x 204/I =  dx 2008 2008 sin x  cos x   x2 1 dx x2  sin x 207/I =  dx cos x  208/I =  cos x.cos 4x dx 1 dx 2x  ex 0e e ln x 210/I =  dx (x  1) 209/I =  e 1 211/I =  dx x 1  x x3 218/I =  ln 219/I =  dx 1 x  ex dx  ex 220/I =  x  x dx dx 1 x 1 x2 217/I =  dx 11 x 205/I =  sin x.ln(1  cos x) dx 206/I =  203/I =   x2 221/I =  x  1dx  222/I =  (cos3 x  sin x) dx x2 1 223/I =  dx x  1 224/I =  (1  x) e 2x dx  225/I =  226/I =  ThuVienDeThi.com cos x cos x  x 1 dx 3x  dx   sin 2x  cos 2x dx cos x  sin x 227/I =    sin 2x  sin x dx cos3x  242/I =  (1  e x ) 228/I =  dx 2x  e  sin 2x dx 2 sin x  2cos x 243/I =  229/I =  x (1  x)3 dx  230/I = 2 244/I = sin x.cos x  cos x  dx 231/I =  x  3x   2 245/I = 4x  1 246/I = 232*/I =  x sin x.cos xdx 247/I =  cos x 233/I =  dx cos 2x  234/I =  dx x (x  1)  2 248/I =  x x2  dx 1 x2 dx x2 x2 4x dx x x 1 dx sin x dx  sin x  dx   240*/I =  ln( x  a  x)dx 1 cos x dx  cos 2x 252/I =  dx (1  x)x x 1 253/I =  dx 3x  251/I =   cos x cos x  cos xdx  1 x 250/I =  238/I =  x sin x cos xdx 239/I = x3 dx  236/I =  1 x 249/I =  x (1  x )6 dx   235/I =  sin 2x(1  sin x) dx  2  237/I =  dx x 1 dx 3x   x3  cos x  sin x dx  sin 2x  254*/I =    sin x 241/I =  dx x (1  cos x)e ThuVienDeThi.com    cos x cos x  cos xdx 255/I =   sin x dx cos x  267/I =  2 268/I =  256/I =  tg xdx    sin x 257*/I =   cos x 269/I =  sin x cos x(1  cos x) dx e x dx 258/I =  (1  x )3 dx  259/I =  x.tg xdx dx 2 (4  x ) 3x dx 261/I =  x 2  x5 262*/I =  dx x(1  x ) 260/I=   cos x dx  sin x 263/I =   sin x dx 264/I =  cos x  sin x  sin x dx 265/I =  cos 2x  dx sin x  cos x  265/I =   sin x  cos x 270/I =  dx sin x  cos x   sin x  cos x dx 271/I =  sin x  cos x   sin x cos x  cos x dx sin x  272/I =  273/I =  266/I =  x (1  x ) dx 1 ex dx x3 x  2x  10x  274/I =  dx x  2x  x3 275/I =  dx (x  1) 276/I =  dx x 1 x 1 277*/I =  dx x  1 x 278/I =  dx (2x  1) 279/I =  dx  x  a 3   sin x dx x 280/I =  ThuVienDeThi.com x 1 x dx 281*/I =  x ln(x   x ) 1 x 2 295/I = dx 282/I =  (x  1) ln x dx 296/I =  287/I =   298/I =   12x  4x x  1 x 299/I =  dx dx dx x  1 x dx cos x dx cos x   cos x dx  cos x   sin x dx sin x  303/I =  290/I =  (cos3 x  sin x)dx   cos3 x 304/I =  dx cos x  291/I =  cos5 x sin xdx  292/I =  cos 2x(sin x  cos x)dx 305/I =  2cos x  sin x  dx 0   cos x  (1  cos x)2 dx 306/I =   294/I =  dx  cos x  1 x dx  302/I =  dx  sin x x 1 x x3 dx  sin x cos x cos x  sin x dx  sin 2x  293/I =  dx 300/I =  289/I =   dx  301/I =   1 x 1  cos x dx  cos 2x 288/I =  0x 1 1 (3  2x)  297*/I =  3x dx x  2x  1 4x  285/I =  dx x  2x  x  286/I = x3 283/I =  x ln(x  1) dx x x 1 284/I =    307/I =  tg x dx ThuVienDeThi.com  1 308*/I =  dx 2x  e 1  sin x 309*/I =  x dx   321*/I =  tg x dx  322/I =  cotg x dx    sin x dx 310*/I =  cos x  sin x  323/I = sin x dx cos x  sin x 311/I =   4  tgx 312*/I =   ln (cos x)  dx  sin x 325/I =  dx cos x  sin x dx cos x  sin x 1 314*/I =  x dx   (e 1)(x 1) 1 313*/I =  315*/I =  e 316*/I =   3x 1 x  cos 2x dx  cos 2x  326/I =  dx  327*/I =  ( x 4 dx cos3 x 317*/I =  dx cos  3cos x  x t 2et 318*/Tìm x> cho  dt  (t  2)  319*/I =   1   tgx dx 324*/I =   tg x dx cos x cos x  x dx x 1 328*/I =  2 329*/I =  ln 330/I = tan x  dx 320*/I =  3x  6x  1dx x x 333*/I =  ln(1  tgx)dx ThuVienDeThi.com dx dx  x cos (ln x  1) e  x  x3 dx x4 ex (e  1) e   1 e4 331/I = t gx  ) dx tgx  ThuVienDeThi.com ... 320*/I =  3x  6x  1dx x x 333* /I =  ln(1  tgx)dx ThuVienDeThi.com dx dx  x cos (ln x  1) e  x  x3 dx x4 ex (e  1) e   1 e4 331/I = t gx  ) dx tgx  ThuVienDeThi.com ... sin x  cos x 75/I =  e 76/I =  cos(ln x)dx 77*/I =   x dx x dx  x  1 78/I =  ThuVienDeThi.com  3ln x ln x dx x e 79/I =  80/I =  ln(x  x)dx  cos x dx  5sin x  sin x 94/I =  e2...  1) x4 106*/I =  dx x 1  104*/I =  2 107/I =  x sin xdx 2 108/I =  x cos xdx ThuVienDeThi.com  109/I =  x.sin x cos xdx x 2ex 110*/I =  dx (x  2)  111/I =  e 2x sin xdx x 112/I