‹ 333 BÀI TOÁN 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 π 2/Định m ñể 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 : π π 4/I = ∫ 3tg x dx 12 / I = π π π π π − cos x π ∫ sin x dx 14/I = ∫ + cos x dx π π x x dx π sin cos 2 ∫ 15/I = 7/ I = ∫ sin2 x.cos2xdx π 8/I = ∫ π (2cos2 x-3sin2 x)dx 16/I = 9/ I= π ∫ − π π − x ) dx π s in ( + x ) sin ( ∫ − π ∫ π π cotg2x dx 17/I = ∫ esin x sin 2x dx π π 10 / I = sin x − sin x cot gx dx ∫ sin x π 13*/ I = 5/I = ∫ (2cotg x + 5) dx 6/I = ∫ sin x dx π (tgx-cotgx)2 dx 18/ π 11/ I = ∫ cos x dx e tgx + 2 I= ∫ cos x Xuct om ang web chuy˚n n hi v oŸn h c ! π dx x2 − x2 dx 35/I = ∫ 2 x 16 − x 36*/I = ∫ dx 2 x x −9 19/ I = ∫ sin x dx π π ∫0 cos x dx 20/ I = π 2 ∫ cos x(sin 21/I = x + cos x)dx 2 ∫ x − x dx 37/I = −1 π 38/I = ∫ x (x + 4)3 dx 22/ I = ∫ cos3 xdx 0 π ∫ 39/I = 3 − −2 ln 41/I = x dx 26/I = ∫ 2x + 1 27/I = ∫ x dx e + 28/I = ∫ dx −x − e e 2x dx 29/I = ∫ x e +1 e− x dx 30/I = ∫ − x + e e ln x 31/I = ∫ dx x(ln x + 1) 42/I = ∫ 1 π dx x x +1 dx − 2x 43/I = ∫ sin xdx π dx cos x 44*/I = ∫ e−2x 45/I = ∫ − x dx + e ln 46/I = ∫ dx x e +1 π 47/I = ∫ x +1 32/I = ∫ dx 3x + ang web chuy˚n n hi x2 +1 x ∫ e − 1dx 25/I = ∫ x + x dx om ∫ 40*/I = ∫ x − x dx Xuct x2 − dx x 4sin x 23/ I = ∫ dx + cosx 24/ I = ∫ 34/I = π sin v oŸn h c ! x cot gx dx 2 ln x + ln x 48/I = ∫ dx x e 33/I = ∫ (x − 3) x − 6x + dx π e sin(ln x) dx x 49/I = ∫ 64/I = ∫ sin x.sin 2x.sin 3xdx π 50/I = ∫ x (x − 1)5 dx 65/I = ∫ cos 2x(sin x + cos x)dx 51/I = ∫ (1 + 2x)(1 + 3x + 3x )3 dx 52/I = ∫ 1+ x 1x π 3 π 66*/I = ∫ ( cos x − sin x )dx dx x7 dx 67/I = ∫ + x − 2x 53/I = ∫ tg x + cot g x − 2dx π 4cos x − 3sin x + dx 4sin x 3cos x + + π 68*/I = ∫ 54/I = ∫ (1 − x )3 dx 69/I = ∫ x − xdx 1 dx 2x +3 0e ln ex 55*/I = ∫ 56/I = ∫ (e + 1) x x +1 dx 3x + π x 71*/I = ∫ sin dx 2 x 72*/I = ∫ dx + x + − x 70/I = ∫ dx 57/I = ∫ x(e 2x + x + 1)dx −1 π 58/I = ∫ − cos3 x sin x.cos5 xdx ∫ x + x dx 73/I = 0 ∫ 59*/I = π x x2 + ln(1 + x) dx x + 1 74**/I = ∫ dx π sin x dx sin x + cos x x 60/I = ∫ dx + cos 2x ln 61/I = ∫ ln Xuct om 75/I = ∫ eπ e 2x 76/I = ∫ cos(ln x)dx dx e −1 x ang web chuy˚n n hi v oŸn h c ! x2 +1 62/I = ∫ ln xdx x e 77*/I = ∫ + x dx x2 dx (x + 1) x + 1 x dx 1 + x −1 78/I = ∫ 63/I = ∫ + 3ln x ln x dx x e 79/I = ∫ π cos x dx − 5sin x + sin x 94/I = ∫ 80/I = ∫ ln(x − x)dx e2 95*/I = ∫ ( e e 81/I = ∫ (ln x) dx 82/I = ∫ e −4 ln x dx x −1 3π ln x 83/I = ∫ dx ln x ∫ cos 2x + 1dx 98/I = π π 84/I = ∫ x ln(x + 1)dx 99/I = ∫ cos x ∫ x + dx 1 86/I = ∫ dx 4−x 85/I = sin xdx 2π 100/I = ∫ + sin xdx 3π π2 101/I = π ln(sin x) 102/I = ∫ − sin xdx ∫ sin xdx 88/I = ∫ cos x π dx π x sin x dx + cos x 1 105*/I = ∫ dx x −1 (x + 1)(4 + 1) 104*/I = ∫ 90*/I = ∫ ln( + x − x)dx ang web chuy˚n n hi 103/I = ∫  ln(x + x + 1)  dx   −1 om ∫ sin 2x dx π π 89/I = ∫ cos(ln x)dx Xuct ∫ x − 2x − x + dx 97/I = e2 87/I = ∫ x − dx 96/I = e2 1 − )dx ln x ln x v oŸn h c ! 91*/I = ∫ x4 106*/I = ∫ dx x + −1 1 2 x −1 x +1 92/I = ∫ dx x x3 dx 93/I = ∫ x − 16 dx π2 107/I = ∫ x sin xdx π2 108/I = ∫ x cos xdx π dx x − 4x − 5 124/I = ∫ dx x − 6x + 1 125/I = ∫ dx −5 2x + 8x + 26 2x + 126/I = ∫ dx x + 127/I = ∫ dx x (x + 1) 123/I = ∫ 109/I = ∫ x.sin x cos xdx x 2ex 110*/I = ∫ dx (x + 2) π 111/I = ∫ e 2x sin xdx x 112/I = ∫ x ln(1 + )dx e ln x dx (x + 1) 113/I = ∫ 128*/I = e 2 1+ x 114/I = ∫ x.ln dx − x x −3 dx (x 1)(x 3x 2) + + + 4x 130/I = ∫ dx (x + 1) 1 131/I = ∫ dx (x + 4x + 3) 129/I = ∫  ln x  115/I = ∫   dx ⇒ I < x   t π 116/I = ∫ sin x.ln(cos x)dx π π e2 117/I = sin 2x dx ∫ −π (2 + sin x) sin x dx (sin x + 3) 132/I = ∫ ∫ cos (ln x)dx Xuct om ang web chuy˚n n hi v oŸn h c ! π π 4sin x dx 133/I = ∫ π − cos x 118/I = ∫ dx cos x π π dx cos x 119*/I = ∫ 1 dx π cos x.sin x 134/I = ∫ 120/I = ∫ x 3e x dx π 121/I = ∫ e sin x π 135/I = ∫ sin x.tgxdx sin x cos xdx π π 136/I = sin 2x dx + cos x 122/I = ∫ π π sin x 137/I = ∫ dx 2 (tg x + 1) cos x 152/I = π 153/I = − 139/I = 140/I = cos x − 155/I = + sin x x + + (x + 4) dx cos x ∫ cos4 x + sin x dx 156/I = ∫ cos x 141/I = ∫ dx sin x cos x + + 142/I = ∫ dx x (x + 1) 1 −3 x 9+x dx π ∫ + 3cos x dx ∫ ∫ 1+ e 2x 154/I = ∫ e x sin xdx π 143/I = ∫ + e 2x π ∫ cos x + dx π − π 2 3e 4x dx 138/I = ∫ 2 π sin x + 9cos x π ∫ sin 2x dx π dx x+9 − x 157/I = ∫ x sin xdx π 158/I = ∫ x cos xdx dx 159/I = ∫ cos x dx Xuct om ang web chuy˚n n hi v oŸn h c ! π 144/I = ∫ 1 160/I = ∫ sin x dx sin x dx cos x π2 145/I = ∫ x − xdx x−4 dx x + x + 147/I = ∫ dx −1 x + 2x + dx 148/I = ∫ 4x − x π 146/I = ∫ 162/I = 163/I = ∫ x cos x sin x dx π 164/I = ∫ 4x − x + dx −1 ∫ 150/I = −2 151/I = ∫ π 2x − x + 4x + 13 dx x 3+ e 165/I = ∫ e dx dx 166/I = ∫ e3x sin 4x dx π sin 2x dx + cos x 183/I = ∫ dx x − 6x + 1 x + 3x + dx 184/I = ∫ x +3 185/I = ∫ dx x (x + 1) ln(1 + x) dx 186/I = ∫ x + 1 1+ x4 dx 187/I ∫ + x 182/I = ∫ x 2ex dx (x + 2) 168/I = ∫ 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 1 e2 188/I = ∫ x15 + x dx 1 173/I = ∫ ( − )dx ln x e ln x ang web chuy˚n n hi x π om ∫ x cos x sin x dx 167/I = ∫ e2x sin x dx Xuct ∫ x cos x dx π 149/I = ∫ x sin x dx 161/I = v oŸn h c ! 2 189/I = ∫ 175/I = ∫ x ln(1 + ) dx x ln x 176/I = ∫ dx x e ln x dx 177/I = ∫ (x + 1) 178/I = ∫ x ln π 190/I= π sin 2x.cos x dx + cos x 192/I = ∫ 1+ x dx 1− x π sin 2x + sin x dx + 3cos x 193/I = ∫ π − 2sin x dx + sin 2x 194/I = ∫ 3 sin x cos x dx π ∫ 195/I = 181/I= ∫ ln x dx 180/ ∫ e π sin 2x ∫ + sin x dx 196/I = ∫ x −1 ) dx x+2 212/I = ∫ π 197/I = ∫ ( −1 π dx tgx cos x + cos x dx x4 214/I = ∫ dx x −1 −3 π 2 dx ∫ −1 x + + x dx 201/I = ∫ x+2 + 2−x 200/I = sin 3x dx + cos x 215/I = ∫ 2 216/I = ∫ ang web chuy˚n n hi x +1 2 199/I = ∫ ( x + − x − ) dx om x + 2x x2 dx − x x 213/I = ∫ dx 4−x 198/I = ∫ x.tg x dx Xuct dx 191/I = ∫ (esin x + cos x) cos x dx π sin x −x e π 179/I = ∫ cos x.ln(1 − cos x) dx π e +e x e e ex 174/I = ∫ (x + x) ln x dx v oŸn h c ! x2 1− x2 dx ln(1 + x) 202/I = ∫ dx x2 1− x2 dx 217/I = ∫ + x 2 π sin 2x dx + cos x 218/I = sin 2008 x 204/I = ∫ dx 2008 2008 + sin x cos x 219/I = 221/I = ∫ x + 1dx x +1 dx x2 π π sin 222/I = ∫ (cos3 x + sin x)dx x dx cos x 207/I = ∫ x2 +1 223/I = ∫ dx x +1 π 208/I = ∫ cos x.cos 4x dx 224/I = ∫ (1 + x) e 2x dx π 209/I = ∫ 2x dx x e + e e ln x 210/I = ∫ dx (x + 1) e 211/I = ∫ π 226/I = ∫ dx x +1 + x x +1 dx 3x + 242/I = ∫ π + sin x dx cos3x + sin 2x dx + sin x 2cos x 243/I = ∫ 2 229/I = ∫ x (1 − x)3 dx 244/I = ∫ ang web chuy˚n n hi dx π sin 2x + cos 2x dx cos x + sin x om cos x + (1 + e x ) 228/I = ∫ dx 2x + e Xuct cos x 225/I = ∫ π + sin 2x 227/I = ∫ dx 1+ x2 − ex dx + ex 220/I = ∫ x − x dx 205/I = ∫ sin x.ln(1 + cos x)dx ∫ ∫ π 206/I = ∫ ln π x3 203/I = ∫ v oŸn h c ! x3 1− x2 dx π sin x.cos 2 x 230/I = ∫ dx cos x + 1 x − 3x + 2 246/I = dx 232*/I = ∫ x sin x.cos xdx 247/I = ∫ π 2 cos x dx + cos 2x 234/I = ∫ dx x (x + 1) 233/I = ∫ 248/I = π x x +9 dx dx π cos x + sin x dx + sin 2x π π 254*/I = ∫ −1 − sin x dx x (1 + cos x)e 241/I = ∫ π sin x dx cos x + 267/I = ∫ π Xuct x x2 −1 cos x dx + cos 2x 252/I = ∫ dx (1 + x)x x +1 253/I = ∫ dx 3x + ∫ cos x cos x − cos xdx π2 ∫ cos x cos x − cos xdx − dx 251/I = ∫ 240*/I = ∫ ln( x + a + x)dx 255/I = − x2 π π π x2 sin x dx sin x + 238/I = ∫ x sin x cos xdx − 1− x2 dx x2 250/I = ∫ 236/I = ∫ dx π 2 ∫ 1− x 249/I = ∫ x (1 − x )6 dx 235/I = ∫ sin 2x(1 + sin x)3 dx x +1 dx 3x + ∫ π 239/I = ∫ 2 π 237/I = ∫ 4x − 231/I = ∫ 245/I = x3 268/I = π om ∫ ang web chuy˚n n hi v oŸn h c ! sin x dx x 10 π π 269/I = ∫ sin x cos x(1 + cos x) dx 256/I = ∫ tg xdx π π + sin x 257*/I = ∫ + cos x π sin x − cos x 270/I = ∫ dx + + sin x cos x e x dx π 258/I = ∫ (1 − x )3 dx sin x − cos x 271/I = ∫ dx + + sin x cos x 0 π π 259/I = ∫ x.tg xdx sin x cos x + cos x dx sin x + 272/I = ∫ dx 2 (4 + x ) 3x 261/I = ∫ dx x +2 − x5 dx 262*/I = ∫ x(1 x ) + 260/I= ∫ 273/I = ∫ dx x a 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 2 + x +1 π cos x dx − sin x 263/I = ∫ π sin x dx cos x 264/I = ∫ π sin x + sin x dx cos 2x 265/I = ∫ π dx π sin x + cos x 265/I = ∫ 3 266/I = ex 280/I = ∫ dx ∫ x (1 + x ) 295/I = ∫ om ang web chuy˚n n hi x 1− x dx Xuct v oŸn h c ! x x −1 dx 11 281*/I = ∫ x ln(x + + x ) 1+ x dx 297*/I = ∫ 1 283/I = ∫ x ln(x + 1) dx 298/I = ∫ 3x dx x + 2x + 1 4x − 285/I = ∫ dx x + 2x + x + 2 286/I = −1 (3 + 2x) 287/I = ∫ π 299/I = x + 1+ x dx x + 1+ x2 dx cos x dx cos x + dx π cos x dx − cos x 302/I = ∫ π sin x dx sin x + 303/I = ∫ π π cos3 x 304/I = ∫ dx cos x + 290/I = ∫ (cos3 x + sin x)dx π π 305/I = 291/I = ∫ cos5 x sin xdx ∫ 2cos x + sin x + dx π 292/I = ∫ cos 2x(sin x + cos x)dx π π 293/I = ∫ dx + sin x ang web chuy˚n n hi cos x ∫ (1 − cos x)2 dx 306/I = π om dx 301/I = ∫ cos x + sin x 289/I = ∫ dx + sin 2x π Xuct −1 + π π + 1+ x dx dx sin x cos x π cos x 288/I = ∫ dx cos 2x + 0 π x 1+ x x3 300/I = ∫ + 12x + 4x ∫ 1+ x dx π ∫ 0x 284/I = ∫ ∫ 282/I = ∫ (x − 1) ln x dx x3 296/I = 307/I = ∫ tg3 x dx v oŸn h c ! 12 π π dx − cos x 321*/I = ∫ tg5 x dx 294/I = ∫ π 1 dx ∫ 2x −1 + e π sin x dx 309*/I = ∫ x + −π 322/I = ∫ cotg x dx 308*/I = π π 323/I = π π sin x dx 310*/I = ∫ cos x sin x + π π sin x dx 4 + cos x sin x tgx 312*/I = ∫ − ln (cos x) 0 π sin x dx cos x + 325/I = ∫ dx π cos 2x dx π − cos 2x 326/I = ∫ π sin x dx + cos x sin x 1 314*/I = ∫ x dx (e 1)(x 1) + + −1 313*/I = ∫ 315*/I = ∫ e 316*/I = ∫ π 3x +1 x π 327*/I = ∫ ( 1 2 dx 329*/I = ∫ cos x dx cos − 3cos x + x t 2et 318*/Tìm x> cho ∫ dt = (t + 2) 317*/I = ∫ π 319*/I = ∫ π ln 3 tan x cos x cos x + 330/I = ∫ x − x3 dx x4 ex (e + 1) e − π −1 e4 331/I = t gx − ) dx tgx + x dx x3 + 328*/I = ∫ dx x2 + ∫ + tgx dx 324*/I = 311/I = ∫ π ∫ tg x dx x x dx dx ∫ x cos (ln x + 1) e π dx 333*/I = ∫ ln(1 + tgx)dx Xuct om ang web chuy˚n n hi v oŸn h c ! 13 320*/I = ∫ −3x + 6x + 1dx Xuct om ang web chuy˚n n hi v oŸn h c ! 14