333 Bài toán tích phân luyện thi đại học

<span class='text_page_counter'>(1)</span>333 BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC 1/ Cho hàm số : f(x)= x.sinx+x2 . Tìm nguyên hàm của hàm số g(x)= x.cosx biết rằng nguyên hàm này triệt tiêu khi x=k  2/Định m để hàm số: F(x) = mx 3 +(3m+2)x2 -4x+3 là một nguyên hàm của hàm số: f(x) = 3x2 +10x-4. 3/Tìm họ nguyên hàm của hàm số: f(x)= cos 3 x.sin8x. TÍNH :  3. 4/I =  3tg 2 x dx. 3  sin x dx. 12 / I =.  4  4. 0.  2 3. sin 3 x  sin x 13*/ I =  cot gx dx sin x . 5/I =  (2cotg 2 x  5) dx. 6/I =.  2.  6  2 1  cos x.  1  cos x dx. 3.  2. 4  sin x dx. 14/I =. 0. 0. . . 3. 1 x x dx sin 2 cos 2 4 2 2.  . 15/I =. 2. 7/ I =  sin2 x.cos2xdx 0.  . 3. 8/I =. . (2cos2 x-3sin2 x)dx. 0. 9/ I=.  2. .  2.   x) 4 dx  sin(  x) 4. 4. 16/I =.  2. 17/I =  esin. . x. sin 2x dx. . 18/. 6. 11/ I =  cos 4 x dx. e tgx  2 2 I=  0 cos x 4. (tgx-cotgx)2 dx.  4 0. 2.  4. 3. . cotg2x dx. 6. sin(. . 10 / I =. . . .. 1. 34/I =. . 3. Lop10.com. 1 x. 2. 4x. 2. dx.

<span class='text_page_counter'>(2)</span> . 4. 35/I = . 2. 1 19/ I =  sin 4 x dx . 2. 36*/I =. 4 . 1.  cos. 6. 0. x. dx. 2. 4 4  cos 2 x(sin x  cos x)dx. 37/I =. 22/ I =  cos xdx 0  2. 4sin 3 x 23/ I =  dx 1  cosx 0 1. 3 2  x 1  x dx. 24/ I =. 25/I =  x. 5. 2. 1  x dx. 0. x dx 2x  1 0 1 1 27/I =  x dx 0e 4 2 1 28/I =  dx x 11 e 2 e 2x dx 29/I =  x 0 e 1 1 e x dx 30/I =   x 1 0e e ln x 31/I =  dx 2 x(ln x  1) 1 7 3. 32/I = . 0 2. x2  4 dx x. x 1 dx 3 3x  1. . 39/I =. 4 3 3.  2. . 40*/I =. 2 ln 2. 41/I =. x2 1. dx x x 1 2. x  e  1dx. 0 1. 42/I = . 0  2. 0 1. 26/I = . x x 9. dx. 38/I =  x (x 2  4)3 dx. 0 1. 2. 2 2  x 4  x dx. 4. 3. dx. 1 2. 0.  2. . 2. 2. . 21/I =. x 16  x 6 1 2 3. 4. 20/ I =. 1. 1 dx 3  2x. 43/I =  sin 5 xdx 0.  3. 1 dx cos x 0. 44*/I = . e 2x dx 45/I =   x e  1 0 ln 3 1 dx 46/I =  x 0 e 1 1.  4. 47/I = .  6. 1 2. sin x cot gx. dx. ln x 3 2  ln 2 x 48/I =  dx x 1 e. .. 3. 33/I =  (x  3) x 2  6x  8 dx 0. .. Lop10.com.

<span class='text_page_counter'>(3)</span>  2. e. sin(ln x) dx x 1. 64/I =  sin x.sin 2x.sin 3xdx. 49/I = . 0  2. 1. 50/I =  x 3 (x 4  1)5 dx 0 1. 65/I =  cos 2x(sin 4 x  cos 4 x)dx 0. 2 3. 51/I =  (1  2x)(1  3x  3x ) dx 0 2. 1. 52/I = . 1 x. 1x  3. 3. 66*/I =  ( 3 cos x  3 sin x )dx 0. dx. x7 dx 67/I =  8 4 1  x  2x 2 3. 53/I =  tg 2 x  cot g 2 x  2dx  6 1.  2. 4cos x  3sin x  1 dx 4sin x  3cos x  5 0. 68*/I = . 54/I =  (1  x 2 )3 dx. 9. 69/I =  x. 3 1  xdx. 0. 1 2. 1. 1 55*/I =  2x dx e  3 0 ln 3 ex 56/I =.  2. . x. (e  1). 0. 3. x 1 dx 3 0 3x  2  x 71*/I =  sin 6 dx 2 0 2 x 72*/I =  dx 2  x  2  x 0 70/I = . dx. 0. 57/I =  x(e 2x  3 x  1)dx 1  2 6. 3. 3. 5. 58/I =  1  cos x sin x.cos xdx. 73/I =. 0. 0. 2 3. 59*/I =. . 5. 1 2. x x 4. dx. x 60/I =  dx 1  cos 2x 0. . e. 2x. dx x ln 2 e  1 e 2 x 1 .ln xdx 62/I =  x 1 61/I =. x2 63/I =  dx (x  1) x  1 0 1. ln(1  x) dx 2 x  1 0. 1.  4. ln 5. 3 2  x . 1  x dx. 74**/I =   2. sin x dx sin x  cos x 0. 75/I = . e. 76/I =  cos(ln x)dx 1 2. 77*/I =  4  x 2 dx 0. 2. x dx 1  x  1 1. 78/I =  .. Lop10.com.

<span class='text_page_counter'>(4)</span> 1  3ln x ln x 79/I =  dx x 1.  6. e. cos x dx 2 6  5sin x  sin x 0. 94/I = . 3. 80/I =  ln(x 2  x)dx 2. e2. 95*/I =  ( e. e. 3. 2. 96/I =. 81/I =  (ln x) dx e. 82/I =. ln x dx x.  e. e2. 83/I =. 97/I =  x 3  2x 2  x  2 dx. ln x dx ln x. . 1 2. 98/I =. 84/I =  x ln(x 2  1)dx 1 3. 85/I =. 1. 1. 86/I = . 4x. 0. 2.  cos 2x  1dx.  4 . 99/I =  cos x 100/I =. dx 101/I =.  4. 88/I = . 2. cos x.  6 2.  sin 2x dx. 102/I =  1  sin xdx. dx. 0 1. 1. 2. 90*/I =  ln( 1  x 2  x)dx 0 3. . 1 2. x 1 x 1 92/I =  dx x 1 3 x3 dx 93/I =  2 x  16 1 2 3 8. dx. 3. 103/I =   ln(x  x 2  1)  dx   1 . 89/I =  cos(ln x)dx. 91*/I =.  1  sin xdx. 0 3 4.  4 .  sin xdx. 0  3 ln(sin x). sin xdx. 2. 2. 87/I =. 1 3 4. 0.  x 2  3 dx 3. 1. 2  x  4 dx. 4 2. 1. 2. 1 1  )dx ln 2 x ln x. x sin x dx 2 1  cos x 0 1 1 105*/I =  2 dx x 1 (x  1)(4  1) 1 x4 dx 106*/I =  x 1 1  2 104*/I = . 107/I =. 2 4.  x sin xdx. 0. 108/I =. 2 4.  x cos xdx. 0. .. Lop10.com.

<span class='text_page_counter'>(5)</span>  6. 1. 2. 109/I =  x.sin x cos xdx 0. x 2ex dx 110*/I =  2 (x  2) 0 1. . 111/I =  e 2x sin 2 xdx 0. 2. 1 x. 112/I =  x 2 ln(1  )dx 1. 3 dx x  4x  5 0 2 5 124/I =  2 dx 1 x  6x  9 1 1 125/I =  dx 2 2x  8x  26 5 1 2x  9 126/I =  dx x  3 0 4 1 127/I =  2 dx x (x  1) 1 123/I = . 2. e. ln x dx 2 1 (x  1). 113/I = . e 1 2. 0. 128*/I =. 2. 114/I =  x.ln 0. 129/I = . 2.  ln x  115/I =    dx  I  2 x   1  3. 116/I =  sin x.ln(cos x)dx 0.  3. sin 3 x 132/I =  dx 2 (sin x  3) 0.  e2. 2  cos (ln x)dx.  3. 1  4. 4sin 3 x 133/I =  dx  1  cos x. 1 dx cos x 0. 118/I = . 6  3.  4. 1 dx 2 cos x.sin x . 1 dx 3 cos x 0. 134/I = . 119*/I =  1. x 3 dx 2 (x  1)(x  3x  2) 0 1 4x 130/I =  3 dx (x  1) 0 1 1 131/I =  4 dx 2 (x  4x  3) 0 1. 1 x dx 1 x. t. 117/I =. 6  3. 3 x2. 120/I =  x e dx 0  2. 121/I =  e 0  2. sin 2x. dx  2  (2  sin x). 135/I =  sin x.tgxdx sin 2 x. 3. .sin x cos xdx. sin 2x 122/I =  dx 4 0 1  cos x. 136/I =. 0  3  4. .. Lop10.com. 1.  sin 2x dx.

<span class='text_page_counter'>(6)</span>  4. 3. sin x 137/I =  dx 2 2 5 (tg x  1) .cos x 0 138/I =.  3. 152/I =. 139/I =. 140/I =. cos x  1. 1  sin x. 1. 156/I = . 0 . cos x 141/I =  dx sin x  cos x  1 0 4 1 142/I =  2 dx x (x  1) 1 1 1 3. x  4  (x  4).  3. sin 3 x 144/I =  dx cos x 0. 0 . 158/I =  x 2 cos 2 xdx 3. dx. 0 1. 159/I =  cos x dx 0 1. 160/I =  sin x dx 0. 145/I =  x 1  xdx. 161/I =. 0 6. x4 1 146/I =  . dx x  2 x  2 4 0 1 dx 147/I =  2 1 x  2x  9 3 1 dx 148/I =  2 1 4x  x 2.  4x  x  5 dx. 149/I =. 1 2. . 150/I =. 2 1. 151/I = . 0. 2x  5 x 2  4x  13 1 dx x 3 e. 3 dx x9  x. 157/I =  x sin xdx. 1. 2. dx. cos 4 x 155/I =  dx 4 4 cos x  sin x 0.  1  3cos x dx. . x 9x. 2. dx. 0  2. 0  2. 143/I =. 1 e 1. 2x. 154/I =  e x sin 2 xdx.  cos x  2 dx   2  2. . 7  2. . 3  2. . 3e 4x  e 2x. 0 4. 153/I =. 1  sin 2 x  9cos 2 x dx . 1 2. dx. 2 4.  x sin x dx. 0 2. 162/I =.  4.  x cos x dx. 0 . 163/I =  x cos 2 x sin x dx. 164/I =. 0  6. 2  x cos x sin x dx. 0 4. 165/I =  e 1  4. x. dx. 166/I =  e3x sin 4x dx 0. Lop10.com.

<span class='text_page_counter'>(7)</span> . 167/I =  e. 2x. 2. sin x dx. 0 1. x 2ex dx 168/I =  2 (x  2) 0 e. 169/I =  (1  x) ln x dx 1 e. 170/I =  x ln 2 x dx 1 1 e. 171/I =  ln 2 x dx 1 e. 172/I =  x(2  ln x) dx 1. e2. 1 1 )dx 173/I =  ( 2  ln x e ln x.  2. sin 2x dx 4 1  cos x 0 2 5 183/I =  2 dx x  6x  9 1 1 2 x  3x  2 dx 184/I =  x  3 0 4 1 185/I =  2 dx 1 x (x  1) 1 ln(1  x) 186/I =  2 dx x  1 0 1 1 x4 dx 187/I  6 1  x 0 182/I = . 1. 188/I =  x15 1  x 8 dx 0. 2. 174/I =  (x 2  x) ln x dx 1 2. 1 x. 175/I =  x 2 ln(1  ) dx 1 2. ln x 176/I =  5 dx 1 x e ln x 177/I =  dx 2 1 (x  1) e 1 2. 178/I =  x ln 0  2. 1 x dx 1 x. 189/I = . e e. 190/I=. 1 e  2. 191/I =  (esin x  cos x) cos x dx 0  2. sin 2x.cos x dx 1  cos x 0. 192/I = .  2. sin 2x  sin x dx 1  3cos x 0.  4 1  2sin 2. x dx 1  sin 2x. 194/I =  2. x. sin x cos3 x dx. 0.  2. 3. . 195/I =. 0. sin 2x.  1  sin 4 x dx. 0. dx.  ln x dx. 0. 180/  esin. x. 193/I = .  3. 181/I=. x. 0 e. 179/I =  cos x.ln(1  cos x) dx  2. ex. 1.  3. 196/I = .  4. .. Lop10.com. x 5  2x 3 2. x 1. dx. tgx 2. cos x 1  cos x. dx.

<span class='text_page_counter'>(8)</span> x 1 2 197/I =  ( ) dx x  2 1 2.  4. 198/I =  x.tg 2 x dx 0 5. 199/I =  ( x  2  x  2 ) dx 3 4. 2 dx 1 x  5  4 2 x 201/I =  dx x  2  2  x 1 200/I = . ln(1  x) 202/I =  dx 2 x 1 2.  2. sin 2x dx 1  cos x 0. x2 dx 212/I =  2 4  x 0 1 x 213/I =  dx 2 4  x 0 1. 1 2. x4 214/I =  2 dx x  1 0  2. sin 3x dx cos x  1 0. 215/I = . 216/I =. sin 2008 x 204/I =  dx 2008 2008 sin x  cos x 0  2. dx. 2. 1 x 1 x2 dx 217/I =  4 11 x. x3. 7. 218/I =. . 3. 2. dx. 1 x 1  ex dx 219/I =  x 1  e 0 0 ln 2. 220/I =  x 1  x dx 0 1. 0. 3. . x2 1 dx x2. 1  4 sin 3. x 207/I =  dx 2 cos x 0  2. 208/I =  cos 2 x.cos 4x dx 0 1. 1 dx 2x  ex 0e e ln x 210/I =  dx 2 (x  1) 1 209/I = . e 1. . 1. 205/I =  sin x.ln(1  cos x) dx 206/I =. x2. 0 2. 203/I = .  2. 2 2. 1 211/I =  dx 0 x 1  x. 221/I =  x 2  1dx 0  2. 222/I =  (cos3 x  sin 3 x) dx 0 3. x2 1 dx 223/I =  x  1 0 1. 224/I =  (1  x) 2 .e 2x dx 0  2. 225/I = . 0 7 3. 226/I = . 0. .. Lop10.com. cos x 2. cos x  1. x 1 dx 3 3x  1. dx.

<span class='text_page_counter'>(9)</span>  2 1  sin 2x.  cos 2x dx cos x  sin x. 227/I = .  6 1. (1  e x ) 2 dx 228/I =  2x 1  e 0.  2. sin 2x  sin x dx cos3x  1 0. 242/I = .  4. sin 2x dx 2 2 sin x  2cos x 0. 243/I = . 3. 229/I =  x 2 (1  x)3 dx. 230/I =. 0  2. 244/I =. 3. sin x.cos x 4x  1. 0. x 2  3x  2. 231/I = . . 245/I = 246/I =. 232*/I =  x sin x.cos xdx 0. 247/I = . cos x 233/I =  dx cos 2x  7 0 4 1 234/I =  2 dx 1 x (x  1). 0 2. 248/I =. 3. . x x2  9. dx. 0  2. 3  cos x cos x  cos xdx. . x3 1 x. 2. dx. dx. 1 x2 dx x2 x2 4x 1. 2. 2. dx. x x 1. dx. 0  2. 250/I = . 238/I =  x sin 3 x cos 4 xdx. 239/I =. 1 x. 2. sin x dx 1  sin x 0. 236/I = . 7. x3. 249/I =  x 5 (1  x 3 )6 dx. 0 2. . . 2 3 1. 235/I =  sin 2x(1  sin x) dx. 237/I =. . 2 2 1.  2. x 1 dx 3 0 3x  2 4 1. . 1. 2. 2. 2 2. 0. dx.  2. . 0.  cos 2 x  1 dx 0. 1 2. 2 2.  2 1. 240*/I =  ln( x 2  a  x)dx 1.  2. cos x dx 0 7  cos 2x 4 1 252/I =  dx 2 (1  x)x 1 2 x 1 253/I =  3 dx 3x  2 0 251/I = .  3. cos x  sin x dx 3  sin 2x . 254*/I = .  2. 1  sin x 241/I =  dx x (1  cos x)e 0. 4 .. Lop10.com.

<span class='text_page_counter'>(10)</span>  2.  2. 3.  cos x cos x  cos xdx. 255/I =. .  2. sin x dx 2 cos x  3 0. 267/I = . 2. 268/I =.  3. 256/I =  tg 4 xdx.  2.  4.  2 1  sin x. 257*/I = . 0 1  cos x. 269/I =  sin x cos x(1  cos x) 2 dx. e x dx. 1. 258/I =  (1  x 2 )3 dx 0  4. 259/I =  x.tg 2 xdx 0 2. 1 dx 2 2 (4  x ) 0 1 3x 2 261/I =  dx 3 0 x 2 2 1  x5 dx 262*/I =  5 x(1  x ) 1 260/I= .  3. cos x dx 2 1  sin x 0. 263/I = .  3. sin 2 x 264/I =  dx 6 cos x 0  6. sin x  sin 3 x 265/I =  dx cos 2x 0  2. 1 dx sin x 1  cos x . 265/I = . 3 3. 266/I = .. 1. sin x dx  x 0.  x 6 (1  x 2 ) dx 1. 0  4. sin 4 x  cos 4 x 270/I =  dx 0 sin x  cos x  1  4. sin 4 x  cos 4 x 271/I =  dx 0 sin x  cos x  1  2. sin x cos x  cos x dx sin x  2 0. 272/I =  1. 273/I = . 1 ex. dx x3 x 3  2x 2  10x  1 dx 274/I =  x 2  2x  9 0 1 x3 dx 275/I =  2 3 0 (x  1) 1 3 276/I =  3 dx 0 x 1 1 4 x 1 dx 277*/I =  6 x  1 0 1 x 278/I =  dx 3 (2x  1) 0 7 1 279/I =  dx 2  x  1 2 a 1. 280/I =. 3 2. . 1 2 .. Lop10.com. 1 x 1 x. 2. dx.

<span class='text_page_counter'>(11)</span> 1. 281*/I = . x ln(x  1  x 2 ) 1 x. 0. 2. 295/I =. dx. 4. 282/I =  (x  1) 2 ln x dx. 296/I =. 3x dx 2 x  2x  1 1 1 4x  1 285/I =  3 dx 2 0 x  2x  x  2 286/I =. . 287/I = . 0  2. 5  12x  4x. 1. x  1 x. 1. 298/I = . 299/I =  2. dx. dx. 4  2. 290/I =  (cos3 x  sin 3 x)dx 0  2. 291/I =  cos5 x sin 4 xdx 292/I =  cos 2x(sin 4 x  cos 4 x)dx. 1 dx 2  sin x 0. 293/I = . x 1 x x3. 3.  1 x 1. dx. 2. dx. x  1 x. 2. dx. 1 dx 4  sin x cos x 6  2. cos x dx cos x  1 0.  2. cos x dx 2  cos x 0.  2. sin x dx sin x  2 0. 303/I = .  2. cos3 x 304/I =  dx cos x  1 0 305/I =.  2. 1.  2cos x  sin x  3 dx. 0.  2. cos x.  (1  cos x)2 dx. 306/I =.  3.  2. 1 294/I =  dx 2  cos x 0. dx. 2. 300/I = . 302/I = . 0  2. 1 x 1. dx.  3. cos x  sin x dx 3  sin 2x . 289/I = . 0  2. 3. 1 1 . 301/I = . 0  2. x3. 0x 1. cos x dx 2  cos 2x. 288/I = . x x 1. . 1. 1. 1 (3  2x) 2 1. 2. 297*/I = . 3. 1 2. 2 3. . 0 2. 283/I =  x 2 ln(x  1) dx 284/I = . 1. 7. 1 3 0 2. 2.  4. 307/I =  tg 3 x dx 0. Lop10.com.

<span class='text_page_counter'>(12)</span>  4. 1. 1 308*/I =  dx 2x 3  e 1  sin 2 x dx 309*/I =  x 3  1 . 321*/I =  tg 5 x dx 0.  4. 322/I =  cotg 3 x dx.  2. sin x 310*/I =  dx cos x  sin x 0  2. 323/I =. 4. sin x dx 4 cos x  sin x 0. 311/I = . tgx. 312*/I = . 2. 1  ln (cos x). 0. dx. 0. sin 5 x 325/I =  dx cos x  1 0. sin x dx cos x  sin x 0 1 1 314*/I =  x dx 2 (e  1)(x  1) 1 315*/I =  e 0 1. 316*/I = . 0  2. x 2.  3. cos 2x dx 2 1  cos 2x . 326/I = . 6. dx.  4. 327*/I =  (. 2. x 4. dx. 0 1. cos3 x 317*/I =  dx 4 2 cos  3cos x  3 0 x t 2et dt  1 318*/Tìm x> 0 sao cho  2 (t  2) 0  3. 319*/I = .  4 1. 1.  2  tgx dx.  2. 313*/I = . 3x 1.  4. 324*/I =.  2. 1. 4  tg x dx.  4. 4.  2.  6  3. tan x cos x cos 2 x  1. x dx x 1. 328*/I = . 3. 1 2. 2 3. 329*/I = . 1 ln 3. 330/I =. . 0. dx. 320*/I =  3x 2  6x  1dx. x. x. 1. 333*/I =  ln(1  tgx)dx 0. Lop10.com. dx. dx  2 1 x cos (ln x  1) e  4. 0. x  x3 dx x4 ex. (e  1) e  1.  1 e4. 331/I =. t gx  1 2 ) dx tgx  1.

<span class='text_page_counter'>(13)</span> .. Lop10.com.

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