333 bài toán tích phân luyện thi đại học

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)x 2 -4x+3 là một nguyên hàm của hàm số: f(x) = 3x 2 +10x-4. 3/Tìm họ nguyên hàm của hàm số: f(x)= cos 3 x.sin8x. TÍNH : 4/I = 3 2 4 3tg x dx    5/I = 4 2 6 (2cotg x 5)dx    6/I = 2 0 1 cos x dx 1 cos x     7/ I =  2 0  sin 2 x.cos 2 xdx 8/I =  3 0  (2cos 2 x-3sin 2 x)dx 9 / I = 2 2 sin( x) 4 dx sin( x) 4        10 / I =   3 6   (tgx-cotgx) 2 dx 11/ I = 4 4 0 cos x dx   12 / I = 2 3 0 sin x dx   13*/ I = 3 32 3 sin x sin x cot gx dx sin x     14/I = 2 4 0 sin x dx   15/I =  3 4 22 2 cos 2 sin 1   xx dx 16/I =  4 6   cotg2x dx 17/I = 22 sin x 4 e sin 2x dx    18/ I =  4 0 2 2 cos  x e tgx . 34/I = 1 2 2 3 1 dx x 4 x  19/ I =  2 4 4sin 1   x dx 20/ I =  4 0 6cos 1  x dx 21/I = dxxxnsix )cos(2cos 44 2 0   22/ I = 2 3 0 cos xdx   23/ I = 32 0 4sin x dx 1 cosx    24/ I = 1 3 2 0 x 1 x dx 25/I = 1 5 2 0 x 1 x dx 26/I = 1 0 x dx 2x 1  27/I = 1 x 0 1 dx e 4  28/I = 2 x 1 1 dx 1 e  29/I = 2x2 x 0 e dx e 1  30/I = x1 x 0 e dx e 1     31/I = e 2 1 ln x dx x(ln x 1)  32/I = 7 3 3 0 x 1 dx 3x 1    33/I = 2 3 2 0 (x 3) x 6x 8 dx   . 35/I = 4 2 2 1 dx x 16 x  36*/I = 6 2 2 3 1 dx x x 9  37/I = 2 2 2 1 x 4 x dx   38/I = 2 2 3 0 x (x 4) dx 39/I = 24 4 3 3 x 4 dx x   40*/I = 22 2 2 x 1 dx x x 1      41/I = ln 2 x 0 e 1dx 42/I = 1 0 1 dx 3 2x  43/I = 2 5 0 sin xdx   44*/I = 3 0 1 dx cos x   45/I = 2x1 x 0 e dx e 1     46/I = ln 3 x 0 1 dx e 1  47/I = 4 2 6 1 dx sin x cot gx    48/I = 3 2e 1 ln x 2 ln x dx x   . 49/I = e 1 sin(ln x) dx x  50/I = 1 3 4 5 0 x (x 1) dx 51/I = 1 2 3 0 (1 2x)(1 3x 3x ) dx   52/I = 2 3 1 1 dx x 1 x  53/I = 3 2 2 6 tg x cot g x 2dx     54/I = 1 2 3 0 (1 x ) dx 55*/I = 1 2x 0 1 dx e 3  56/I = xln 3 x 3 0 e dx (e 1)  57/I = 0 2x 3 1 x(e x 1)dx    58/I = 2 6 3 5 0 1 cos x sin x.cos xdx   59*/I = 2 3 2 5 1 dx x x 4  60/I = 4 0 x dx 1 cos2x    61/I = 2xln 5 x ln 2 e dx e 1  62/I = 2e 1 x 1 .ln xdx x   63/I = 21 0 x dx (x 1) x 1   64/I = 2 0 sin x.sin 2x.sin3xdx   65/I = 2 4 4 0 cos2x(sin x cos x)dx   66*/I = 2 3 3 0 ( cos x sin x)dx   67/I = 73 8 4 2 x dx 1 x 2x   68*/I = 2 0 4cos x 3sin x 1 dx 4sin x 3cos x 5       69/I = 9 3 1 x. 1 xdx 70/I = 2 3 0 x 1 dx 3x 2    71*/I = 6 0 x sin dx 2   72*/I = 2 0 x dx 2 x 2 x    73/I = 3 3 2 0 x . 1 x dx 74**/I = 1 2 0 ln(1 x) dx x 1    75/I = 2 0 sin x dx sin x cos x    76/I = e 1 cos(ln x)dx   77*/I = 2 2 0 4 x dx 78/I = 2 1 x dx 1 x 1   . 79/I = e 1 1 3ln x ln x dx x   80/I = 3 2 2 ln(x x)dx 81/I = e 2 1 (ln x) dx 82/I = 2e e ln x dx x  83/I = 2e 1 ln x dx ln x  84/I = 2 2 1 x ln(x 1)dx 85/I = 3 2 3 1 dx x 3  86/I = 1 2 0 1 dx 4 x  87/I = 2 4 0 sin xdx   88/I = 3 2 6 ln(sin x) dx cos x    89/I = 2 1 cos(ln x)dx 90*/I = 2 2 0 ln( 1 x x)dx  91*/I = 3 2 2 1 dx x 1  92/I = 38 1 x 1 dx x   93/I = 33 2 1 x dx x 16  . 94/I = 6 2 0 cos x dx 6 5sin x sin x     95*/I = 2e 2 e 1 1 ( )dx ln xln x  96/I = 3 2 4 x 4 dx   97/I = 2 3 2 1 x 2x x 2 dx     98/I = 3 4 4 cos 2x 1dx    99/I = 0 cos x sin xdx   100/I = 2 0 1 sin xdx   101/I = 3 4 4 sin 2x dx    102/I = 0 1 sin xdx   103/I = 1 3 2 1 ln(x x 1) dx        104*/I = 2 0 xsin x dx 1 cos x    105*/I = 1 2 x 1 1 dx (x 1)(4 1)    106*/I = 41 x 1 x dx 1 2   107/I = 2 4 0 x sin xdx   108/I = 2 4 0 x cos xdx   109/I = 6 2 0 x.sin x cos xdx   110*/I = 2 x1 2 0 x e dx (x 2)  111/I = 2x 2 0 e sin xdx   112/I = 2 2 1 1 x ln(1 )dx x  113/I = e 2 1 e ln x dx (x 1)  114/I = 1 2 0 1 x x.ln dx 1 x    115/I = 2t 1 ln x dx I 2 x         116/I = 3 0 sin x.ln(cos x)dx   117/I = 2e 2 1 cos (ln x)dx   118/I = 4 0 1 dx cos x   119*/I = 4 3 0 1 dx cos x   120/I = 21 3 x 0 x e dx 121/I = 2 2 sin x 3 0 e .sin x cos xdx   122/I = 2 4 0 sin 2x dx 1 cos x    123/I = 1 2 0 3 dx x 4x 5   124/I = 2 2 1 5 dx x 6x 9   125/I = 1 2 5 1 dx 2x 8x 26    126/I = 1 0 2x 9 dx x 3    127/I = 4 2 1 1 dx x (x 1)  128*/I = 0 2 2 sin 2x dx (2 sin x)   129/I = 1 2 0 x 3 dx (x 1)(x 3x 2)      130/I = 1 3 0 4x dx (x 1)  131/I = 1 4 2 0 1 dx (x 4x 3)   132/I = 33 2 0 sin x dx (sin x 3)    133/I = 33 6 4sin x dx 1 cos x     134/I = 3 2 6 1 dx cos x.sin x    135/I = 3 0 sin x.tgxdx   136/I = 3 4 1 dx sin 2x    . 137/I = 34 2 2 5 0 sin x dx (tg x 1) .cos x    138/I = 3 2 2 3 1 dx sin x 9cos x      139/I = 2 2 cos x 1 dx cos x 2       140/I = 2 0 1 sin x dx 1 3cos x     141/I = 2 0 cos x dx sin x cos x 1     142/I = 4 2 1 1 dx x (x 1)  143/I = 1 3 3 1 dx x 4 (x 4)     144/I = 33 0 sin x dx cos x   145/I = 1 0 x 1 xdx 146/I = 6 4 x 4 1 . dx x 2 x 2     147/I = 0 2 1 1 dx x 2x 9    148/I = 3 2 1 1 dx 4x x  149/I = 2 2 1 4x x 5 dx    150/I = 2 2 2 2x 5 dx x 4x 13     151/I = 1 x 0 1 dx 3 e  152/I = 1 4x 2x2 2x 0 3e e dx 1 e    153/I = 4 2 7 1 dx x 9 x  154/I = 2 x 2 0 e sin xdx   155/I = 42 4 4 0 cos x dx cos x sin x    156/I = 1 0 3 dx x 9 x   157/I = 0 xsin xdx   158/I = 2 2 0 x cos xdx   159/I = 1 0 cos x dx 160/I = 1 0 sin x dx 161/I = 2 4 0 x sin x dx   162/I = 2 4 0 x cos x dx   163/I = 2 0 x cos xsin x dx   164/I = 6 2 0 x cos xsin x dx   165/I = 4 x 1 e dx 166/I = 4 3x 0 e sin 4x dx   167/I = 2x 2 0 e sin x dx   168/I = 2 x1 2 0 x e dx (x 2)  169/I = e 1 (1 x) ln x dx 170/I = e 2 1 x ln x dx 171/I = 1 e 2 1 ln x dx 172/I = e 1 x(2 ln x)dx 173/I = 2e 2 e 1 1 ( )dx ln xln x  174/I = 2 2 1 (x x)ln x dx 175/I = 2 2 1 1 x ln(1 )dx x  176/I = 2 5 1 ln x dx x  177/I = e 2 1 e ln x dx (x 1)  178/I = 1 2 0 1 x x ln dx 1 x    179/I = 2 3 cos x.ln(1 cos x)dx    180/ 2 2 sin x 3 0 e sin x cos x dx   181/I= 2 4 0 sin 2x dx 1 sin x    . 182/I = 2 4 0 sin 2x dx 1 cos x    183/I = 2 2 1 5 dx x 6x 9   184/I = 21 0 x 3x 2 dx x 3     185/I = 4 2 1 1 dx x (x 1)  186/I = 1 2 0 ln(1 x) dx x 1    187/I 41 6 0 1 x dx 1 x    188/I = 1 15 8 0 x 1 x dx 189/I = x1 x x 0 e dx e e  190/I= e 1 e ln x dx 191/I = 2 sin x 0 (e cos x)cos x dx   192/I = 2 0 sin 2x.cos x dx 1 cos x    193/I = 2 0 sin 2x sin x dx 1 3cos x     194/I = 24 0 1 2sin x dx 1 sin 2x     195/I = 5 33 2 0 x 2x dx x 1    196/I = 3 2 4 tgx dx cos x 1 cos x     197/I = 2 2 1 x 1 ( ) dx x 2    198/I = 4 2 0 x.tg x dx   199/I = 5 3 ( x 2 x 2 )dx     200/I = 4 1 2 dx x 5 4    201/I = 2 1 x dx x 2 2 x    202/I = 2 2 1 ln(1 x) dx x   203/I = 2 0 sin 2x dx 1 cos x    204/I = 20082 2008 2008 0 sin x dx sin x cos x    205/I = 2 0 sin x.ln(1 cos x)dx   206/I = 23 2 1 x 1 dx x   207/I = 34 2 0 sin x dx cos x   208/I = 2 2 0 cos x.cos4x dx   209/I = 1 2x x 0 1 dx e e  210/I = e 2 1 e ln x dx (x 1)  211/I = 1 0 1 dx x 1 x   212/I = 21 2 0 x dx 4 x  213/I = 1 2 0 x dx 4 x  214/I = 1 42 2 0 x dx x 1  215/I = 2 0 sin 3x dx cos x 1    216/I = 2 22 2 0 x dx 1 x  217/I = 22 4 1 1 x dx 1 x    218/I = 37 3 2 0 x dx 1 x  219/I = xln 2 x 0 1 e dx 1 e    220/I = 1 0 x 1 x dx 221/I = 1 2 0 x 1dx 222/I = 2 3 3 0 (cos x sin x)dx   223/I = 23 0 x 1 dx x 1    224/I = 1 2 2x 0 (1 x) .e dx 225/I = 2 2 0 cos x dx cos x 1    226/I = 7 3 3 0 x 1 dx 3x 1    . 227/I = 2 6 1 sin 2x cos2x dx cos x sin x       228/I = x 21 2x 0 (1 e ) dx 1 e    229/I = 3 2 3 0 x (1 x) dx 230/I = 32 2 0 sin x.cos x dx cos x 1    231/I = 1 2 2 0 4x 1 dx x 3x 2     232*/I = 2 0 xsin x.cos xdx   233/I = 2 0 cos x dx cos 2x 7    234/I = 4 2 1 1 dx x (x 1)  235/I = 2 2 3 0 sin 2x(1 sin x) dx   236/I = 2 3 0 x 1 dx 3x 2    237/I = 4 2 7 1 dx x x 9  238/I = 3 4 0 xsin x cos xdx   239/I = 2 3 2 cos x cos x cos xdx     240*/I = 1 2 1 ln( x a x)dx    241/I = 2 x 0 1 sin x dx (1 cos x)e     242/I = 2 0 sin 2x sin x dx cos3x 1     243/I = 4 2 2 0 sin 2x dx sin x 2cos x    244/I = 2 32 2 0 x dx 1 x  245/I = 2 32 2 0 x dx 1 x  246/I = 21 2 2 2 1 x dx x   247/I = 21 2 0 x dx 4 x  248/I = 2 2 2 3 1 dx x x 1  249/I = 1 5 3 6 0 x (1 x ) dx 250/I = 2 0 sin x dx 1 sin x    251/I = 2 0 cos x dx 7 cos 2x    252/I = 4 2 1 1 dx (1 x)x  253/I = 2 3 0 x 1 dx 3x 2    254*/I = 3 4 cos x sin x dx 3 sin 2x      . 255/I = 2 3 2 cos x cos x cos xdx     256/I = 3 4 4 tg xdx    257*/I = 2 x 0 1 sin x e dx 1 cos x     258/I = 1 2 3 0 (1 x ) dx 259/I = 4 2 0 x.tg xdx   260/I= 2 2 2 0 1 dx (4 x )  261/I = 21 3 0 3x dx x 2  262*/I = 52 5 1 1 x dx x(1 x )    263/I = 3 2 0 cos x dx 1 sin x    264/I = 23 6 0 sin x dx cos x   265/I = 36 0 sin x sin x dx cos2x    265/I = 2 3 1 dx sin x 1 cos x     266/I = 3 6 2 1 1 dx x (1 x )  . 267/I = 2 2 0 sin x dx cos x 3    268/I = 2 0 sin x dx x   269/I = 2 2 0 sin x cos x(1 cos x) dx   270/I = 4 44 0 sin x cos x dx sin x cos x 1      271/I = 4 44 0 sin x cos x dx sin x cos x 1      272/I = 2 0 sin x cos x cos x dx sin x 2     273/I = 1 1 x 3 a e dx x  274/I = 3 21 2 0 x 2x 10x 1 dx x 2x 9       275/I = 31 2 3 0 x dx (x 1)  276/I = 1 3 0 3 dx x 1  277*/I = 41 6 0 x 1 dx x 1    278/I = 1 3 0 x dx (2x 1)  279/I = 7 2 1 dx 2 x 1   280/I = 3 2 2 1 2 1 dx x 1 x  . 281*/I = 21 2 0 x ln(x 1 x ) dx 1 x     282/I = 4 2 1 (x 1) ln x dx 283/I = 3 2 0 x ln(x 1)dx 284/I = 32 2 1 3x dx x 2x 1   285/I = 1 3 2 0 4x 1 dx x 2x x 2      286/I = 1 2 2 1 2 1 dx (3 2x) 5 12x 4x     287/I = 1 0 1 dx x 1 x   288/I = 2 0 cos x dx 2 cos 2x    289/I = 2 4 cos x sin x dx 3 sin 2x      290/I = 2 3 3 0 (cos x sin x)dx   291/I = 2 5 4 0 cos xsin xdx   292/I = 2 4 4 0 cos2x(sin x cos x)dx   293/I = 2 0 1 dx 2 sin x    294/I = 2 0 1 dx 2 cos x    295/I = 2 2 2 3 1 dx x x 1  296/I = 37 3 2 0 x dx 1 x  297*/I = 2 3 1 1 dx x 1 x  298/I = 31 2 0 x dx x 1 x   299/I = 1 2 1 1 dx 1 x 1 x     300/I = 3 4 6 1 dx sin x cos x    301/I = 2 0 cos x dx cos x 1    302/I = 2 0 cos x dx 2 cos x    303/I = 2 0 sin x dx sin x 2    304/I = 32 0 cos x dx cos x 1    305/I = 2 0 1 dx 2cos x sin x 3     306/I = 2 2 3 cos x dx (1 cos x)     307/I = 4 3 0 tg x dx   . 308*/I = 1 2x 1 1 dx 3 e   309*/I = 2 x sin x dx 3 1     310*/I = 2 0 sin x dx cos x sin x    311/I = 42 4 4 0 sin x dx cos x sin x    312*/I = 2 2 0 tgx dx 1 ln (cos x)    313*/I = 2 0 sin x dx cos x sin x    314*/I = 1 x 2 1 1 dx (e 1)(x 1)    315*/I = 1 3x 1 0 e dx 316*/I = 21 2 0 x dx x 4  317*/I = 32 4 2 0 cos x dx cos 3cos x 3     318*/Tìm x> 0 sao cho 2 tx 2 0 t e dt 1 (t 2)    319*/I = 3 2 4 tan x dx cos x cos x 1     320*/I = 1 2 0 3x 6x 1dx   321*/I = 4 5 0 tg x dx   322/I = 4 3 6 cotg x dx    323/I = 3 4 4 tg x dx    324*/I = 4 0 1 dx 2 tgx    325/I = 52 0 sin x dx cos x 1    326/I = 3 2 6 cos 2x dx 1 cos 2x     327*/I = 4 2 0 t gx 1 ( ) dx tgx 1     328*/I = 1 3 1 2 x dx x 1  329*/I = 3 32 4 1 x x dx x   330/I = xln 3 x x 0 e dx (e 1) e 1   331/I = 1 4e 2 1 e 1 dx x cos (ln x 1)     333*/I = 4 0 ln(1 tgx)dx  