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Giải Tích 12- Chuyên Đề Tích Phân LTĐH *BÀI TẬP LUYỆN THI: Dạng 1: Tích phân các hàm số hữu tỉ 1, 3 2 3 0 I x (1 x) dx= − ∫ 3, 1 2 3 0 I (1 2x)(1 3x 3x ) dx= + + + ∫ 5, 1 0 2x 9 I dx x 3 + = + ∫ 7, 2 1 0 x 3x 2 I dx x 3 + + = + ∫ 9, 2 2 1 5 I dx x 6x 9 = − + ∫ 11, 2 1 2 0 x I dx 4 x = − ∫ 13, 2 2 1 1 I dx x 2x 2 = − + ∫ 15, 1 2 0 4x 1 I dx x 5x 6 + = + + ∫ 17, 1 4 2 2 0 x I dx x 1 = − ∫ 19, 3 2 2 1 3x I dx x 2x 1 = + + ∫ 21, 1 2 0 2 x 2) 1 I dx (x 1) (+ + = ∫ 23, 2 2 1 x 1 I ( ) dx x 2 − − = + ∫ 2, 1 3 4 5 0 I x (x 1) dx= − ∫ 4, 1 5 3 6 0 I x (1 x ) dx= − ∫ 6, 3 0 x 1 I dx 2x 3 + = − ∫ 8, 1 2 0 3 I dx x 4x 5 = − − ∫ 10, 1 2 0 x I dx 4 x = − ∫ 12, 3 3 2 1 x I dx x 16 = − ∫ 14, 2 2 2 1 x I dx x 7x 12 = − + ∫ 16, 1 3 2 1 1 I dx 9x 6x 5 − = + + ∫ 18, 2 3 2 0 3x 2 I dx x 1 + = + ∫ 20, 3 2 3 1 I dx x 3 = + ∫ 22, 1 3 0 3 I dx x 1 = + ∫ 24, 2 1 3 0 2 x 5 I dx x x 1 + + = + ∫ Trang 1 CHUYÊN ĐỀ NÂNG CAO Giải Tích 12 CHUYÊN ĐỀ NÂNG CAO Giải Tích 12 * TÍCH PHÂN LUYỆN THI ĐẠI HỌC * * TÍCH PHÂN LUYỆN THI ĐẠI HỌC * Giải Tích 12- Chuyên đề Tích Phân - LTĐH 25, 3 2 1 2 0 x 2x 10x 1 I dx x 2x 9 + + + = + + ∫ 27, 1 2 5 1 I dx 2x 8x 26 − = + + ∫ 29, 1 3 0 x I dx (2x 1) = + ∫ 31, 2 3 2 1 1 I x x x d x − = + ∫ 33, 5 3 4 2 2 3x x 1 I dx x 2 5x 6 + = − − + ∫ 35, 2 1 4 0 (x 1) I dx (2 x 1) − = + ∫ 37, 1 2 0 2 5x I dx ( 4)x = + ∫ 39, 2 10 2 1 1 I dx x(1 )x = + ∫ 41, 2 3 6 1 x x 1 I dx (1 ) = + ∫ 43, 2 2 4 1 1 x I dx 1 x + = + ∫ 45, 2 2 4 1 1 x I dx 1 x − = + ∫ 47, 7 3 8 4 2 x I dx 1 x 2x = + − ∫ 49, 3 2 3 4 0 x I dx x 1 = − ∫ 51, 1 3 0 4x I dx (x 1) = + ∫ 53, 3 1 2 3 0 x I dx (x 1) = + ∫ 26, 1 2 0 x 3 I dx (x 1)(x 3x 2) − = + + + ∫ 28, 4 2 1 1 I dx x (x 1) = + ∫ 30, 1 3 2 0 4x 1 I dx x 2x x 2 − = + + + ∫ 32, 2 5 3 1 x 1 I dx x = + ∫ 34, 1 3 0 x I dx (x 1) = + ∫ 36, 99 1 101 0 (7x 1) I dx (2x 1) − = + ∫ 38, 2 7 1 5 0 I d x (1 )x x= + ∫ 40, 4 3 4 1 1 I dx x(1 x ) = + ∫ 42, 7 2 7 1 I dx x(1 x x ) 1 = + − ∫ 44, 2 2001 2 1002 1 I dx (1 ) x x = + ∫ 46, 4 1 6 0 x 1 I dx x 1 + = + ∫ 48, 2 1 4 0 x I x dx x 1 = + + ∫ 50, 2 1 5 2 2 4 1 x 1 I dx x 1x + + = − + ∫ 52, 1 4 2 0 1 I dx (x 4x 3) = + + ∫ 54, 2 2 2 0 1 I dx (4 x ) = + ∫ Trang 2 Giải Tích 12- Chuyên Đề Tích Phân LTĐH 55, 4 1 6 0 x 1 I dx x 1 − = + ∫ 56, 5 2 5 1 1 x I dx x(1 x ) − = + ∫ Dạng 2: Tích phân các hàm số vô tỉ 1, 1 0 x 1 xI dx−= ∫ 3, 1 3 2 0 x 1 xI dx−= ∫ 5, 3 3 2 0 x . 1 xI dx+= ∫ 7, 2 2 3 0 I x (x 4) dx= + ∫ 9, 7 3 3 0 x 1 dx 3x 1 I + + = ∫ 11, 2 3 1 1 dx x 1 x I = + ∫ 13, 2 3 2 5 1 I dx x x 4 = + ∫ 15, 2 3 2 2 0 x dxI 1 x− = ∫ 17, 2 2 2 3 1 dx x x 1 I − = ∫ 19, 3 7 3 2 0 x dI x 1 x+ = ∫ 21, 1 0 x dx 2x 1 I + = ∫ 23, 1 2 0 1 x dI x−= ∫ 25, 3 2 2 1 1 I dx x 4 x = − ∫ 2, 9 3 1 x. 1 xI dx−= ∫ 4, 1 15 8 0 I x 1 x dx= + ∫ 6, 1 5 2 0 x 1 xI dx+= ∫ 8, 2 3 2 0 (x 3) x 6x 8 dI x− − += ∫ 10, 2 1 3 0 3x dx x 2 I + = ∫ 12, 1 0 1 dx 3 2x I − = ∫ 14, 4 2 2 1 dx x 16 x I − = ∫ 16, 2 3 0 x 1 I dx 3x 2 + = + ∫ 18, 4 2 7 1 I dx x 9 x = + ∫ 20, 6 2 2 3 1 dx x x 9 I − = ∫ 22, 5 3 3 2 0 x 2x I dx x 1 + = + ∫ 24, 3 8 1 x 1 I dx x + = ∫ 26, 1 2 3 0 (1 x )I dx−= ∫ Trang 3 Giải Tích 12- Chuyên đề Tích Phân - LTĐH 27, 1 2 0 1 I dx 4 x = − ∫ 29, 2 2 2 2 0 x I dx 1 x = − ∫ 31, 1 2 0 x 1I dx+= ∫ 33, 2 2 1 I 4x x 5 dx − − += ∫ 35, 2 3 0 x 1 x x I d 1 + + = ∫ 37, 2 4 4 3 3 d x I x 4 x − = ∫ 39, 4 1 2 dx x 5 4 I − + + = ∫ 41, 2 0 x I dx 2 x 2 x = + + − ∫ 43, 2 1 x I dx 1 x 1 = + − ∫ 45, 1 0 3 I dx x 9 x = + − ∫ 47, 1 3 3 1 I dx x 4 (x 4) − = + + + ∫ 49, 6 4 x 4 1 . dx x 2 x I 2 − + + = ∫ 51, 2 2 2 2 x 1 dx x x 1 I − − + + = ∫ 53, 1 3 1 2 x dx x 1 I + = ∫ 55, 0 2 1 1 dx x 2 I x 9 − + + = ∫ 28, 3 2 2 1 2 1 dxI x 1 x− = ∫ 30, 2 2 2 1 x 4 x dI x − −= ∫ 32, 2 2 0 I 4 x dx= + ∫ 34, 1 2 0 3x 6x 1dxI − + += ∫ 36, 2 1 0 x I dx (x 1) x 1 = + + ∫ 38, 3 2 2 1 I dx x 1 = − ∫ 40, 1 0 1 dx x 1 x I + + = ∫ 42, 7 2 1 dx 2 x 1 I + + = ∫ 44, 3 1 2 0 x I dx x 1 x = + + ∫ 46, 1 2 1 1 I dx 1 x 1 x − = + + + ∫ 48, 2 3 2 1 x 1 dx x I + = ∫ 50, 1 2 2 1 2 1 dx (3 2x) 5 12x I 4x − + + + = ∫ 52, 2 1 2 0 x x I dx 4+ = ∫ 54, 3 3 2 4 1 x x dx x I − = ∫ 56, 3 2 1 1 dx 4x x I − = ∫ Trang 4 Giải Tích 12- Chuyên Đề Tích Phân LTĐH 57, 2 2 2 2x 5 dx x 4x I 13 − − + + = ∫ 59, 2 2 1 x dx 3x 9x 1 I + − = ∫ 61, 4 0 2x 1 dx 1 2x I 1 + + + = ∫ 63, 6 2 1 dx 2x 1 4x I 1+ + + = ∫ 65, 2 5 1 x 1 dx x 3x 1 I + + = ∫ 67, 2 3 0 2x x 1 dx x I 1 + − + = ∫ 69, 0 2 4 I (1 1 2x x 1 x ) d= + + + ∫ 71, 3 2 2 2 0 2 3x x dx x x I x 1 − + − + = ∫ 73, 1 2 1 1 dx 1 x 1 x I − + + + = ∫ 75, 1 3 1 3 4 1 3 x I x (x ) dx − = ∫ 77, 2 27 3 1 I x 2 dx x x+ = − ∫ 79, x I dx x x 3 2 2 2 0 (1 1 ) (2 1 ) = + + + + ∫ 81, 1 3 3 3 0 1 dx ). 1 I (1 x x = + + ∫ 83, 4 2 2 2 3 x dx 1 (x ) x 1 x I − + = ∫ 85, 2 1 6 0 x dx 4 x I − = ∫ 58, 2 1 2 2 2 1 x dx x I − = ∫ 60, 2 2 25 2 ( ) 4 dxI x x x − + −= ∫ 62, 2 1 0 x x dx 1 x x I + + = ∫ 64, 1 0 1 x dx 1 x I + + = ∫ 66, 3 0 x 3 dx 3 x 1 I x 3 − + + + = ∫ 68, 2 1 0 x dx (x 1) x 2 1 I + + = ∫ 70, 1 3 0 2 (x 1) 2x xI x d− −= ∫ 72, 8 2 3 x 1 dx x 1 I − + = ∫ 74, 2 3 2 3 0 I x x dx 4 = + ∫ 76, 2 2 5 2 2 x dx ( 1) x 5 I x + + = ∫ 78, 1 2 0 1 x x x I d 1+ + = ∫ 80, x I dx x x x x 3 2 0 2( 1) 2 1 1 = + + + + + ∫ 82, 3 3 2 2 4 1 x 2015x d x I x x − + = ∫ 84, 2 2 4 1 (3 4 ) d x 2x xI − − = ∫ 86, 2 1 2 0 x dx 3 2 x I x+ − = ∫ Trang 5 Giải Tích 12- Chuyên đề Tích Phân - LTĐH Dạng 3: Tích phân các hàm số lượng giác 1, 3 2 4 I 3tan x dx π π = ∫ 3, 4 2 6 (2cot xI 5)dx π π += ∫ 5, 2 2 0 2 I cosin x. dx xs π = ∫ 7, 2 3 0 2 I 2cos x 3s( dxin x) π = − ∫ 9, 2 4 4 0 I cos2x(sin x cos x)dx π = + ∫ 11, 2 0 I sin x.sin 2x.sin 3xdx π = ∫ 13, 2 2 0 cos x.cos 4x dxI π = ∫ 15, 2 2 3 0 sin 2x(1 sin x) dxI π += ∫ 17, 2 3 2 cos x cos x cosI xdx π π − −= ∫ 19, 3 4 4 tan xdxI π π = ∫ 21, 4 5 0 tan x dxI π = ∫ 2, 2 3 0 I sin x dx π = ∫ 4, 4 4 0 cos x dxI π = ∫ 6, 4 6 I cot 2 x dx π π = ∫ 8, ( ) 3 6 2 tan x cotxI dx π π − −= ∫ 10, 3 2 2 6 tan x cot xI 2dx π π += − ∫ 12, 2 6 3 5 0 1 cos x sin x.cos xdI x π −= ∫ 14, 3 0 sin x.tan xdxI π = ∫ 16, 2 2 0 sin x cos x(1 cos x)I dx π += ∫ 18, 2 5 4 0 cos x sin xdxI π = ∫ 20, 4 3 6 cot x dxI π π = ∫ 22, 3 2 4 tan x dx cos x 1 cos x I π π + = ∫ Trang 6 Giải Tích 12- Chuyên Đề Tích Phân LTĐH 23, 2 4 4 1 I dx sin x π π = ∫ 25, 3 0 1 dx cos x I π = ∫ 27, 4 6 0 1 I dx cos x π = ∫ 29, 4 3 0 1 dx cos x I π = ∫ 31, 3 2 0 4sin x dx 1 cosx I π + = ∫ 33, 2 4 0 sin 2x dx 1 cos x I π + = ∫ 35, 2 0 sin 2x.cos x dx 1 I cos x π + = ∫ 37, 2 0 sin 2x sin x dx 1 I 3cos x π + + = ∫ 39, 2 4 0 1 2sin x dx 1 sin 2x I π − + = ∫ 41, 3 4 2 0 sin x dx cos x I π = ∫ 43, 5 2 0 sin x dx cos 1 I x π + = ∫ 45, 3 2 6 cos 2x dx 1 cos 2x I π π − = ∫ 24, 4 4 4 0 sin x cos x dx sin x cos x 1 I π − + + = ∫ 26, 2 0 sin x cos x cos x dx sin x 2 I π + + = ∫ 28, 2 0 cos x dx 2 cos 2x I π + = ∫ 30, 6 2 0 cos x dx 6 5sin x I sin x π − + = ∫ 32, 2 4 cos x sin x dx 3 sin 2x I π π + + = ∫ 34, 4 2 6 1 dx sin x co I t x π π = ∫ 36, 3 4 2 2 5 0 sin x dx (tan x 1) I .cos x π + = ∫ 38, 3 3 0 sin x dx cos x I π = ∫ 40, 2 4 0 sin 2x dx 1 sin x I π + = ∫ 42, 2 0 sin 2x dx 1 cos x I π + = ∫ 44, 3 3 2 0 sin x dx (sin x 3) I π + = ∫ 46, 0 2 2 sin 2x dx (2 sin x) I −π + = ∫ Trang 7 Giải Tích 12- Chuyên đề Tích Phân - LTĐH 47, 2 6 1 sin 2x cos 2x dx cos x sin x I π π + + + = ∫ 49, 3 2 2 0 sin x.cos x dx co I s x 1 π + = ∫ 51, 3 2 2 3 1 dx sin x 9cos x I π π − + = ∫ 53, 3 4 6 1 dx sin x cos x I π π = ∫ 55, 4 2 2 0 sin 2x dx sin x 2cos x I π + = ∫ 57, 3 6 0 sin x sin x dI x cos 2x π + = ∫ 59, 2 2 0 sin x dx cos x 3 I π + = ∫ 61, 4 0 1 dx 2 tan x I π + = ∫ 63, 2 2 0 cos x dx cos x 1 I π + = ∫ 65, 3 2 4 2 0 cos x dx cos x 3c I os x 3 π − + = ∫ 67, 2 3 1 dx sin x 1 cos x I π π + = ∫ 69, 2 0 sin x dx 1 sin x I π + = ∫ 48, 3 3 6 4sin x dx 1 cos x I π π − = ∫ 50, 3 2 6 1 dx cos x.sin x I π π = ∫ 52, 2 0 sin 3x dx cos 1 I x π + = ∫ 54, 3 2 4 tan x dx cos x cos 1 I x π π + = ∫ 56, 4 2 0 tan x 1 ( ) dx tan 1 I x π − + = ∫ 58, 2 0 sin 2x sin x dx co I s3x 1 π + + = ∫ 60, 3 2 0 cos x dx 1 sin x I π − = ∫ 62, 2 0 4cos x 3sin x 1 dx 4sin x 3cos x 5 I π − + + + = ∫ 64, 2 4 0 sin xdxI π = ∫ 66, 2 0 1 sin x dx 1 3cos x I π + + = ∫ 68, 2 2 cos x 1 dx cos x 2 I π π − − + = ∫ 70, 2 0 cos x dx sin x c I os x 1 π + + = ∫ Trang 8 Giải Tích 12- Chuyên Đề Tích Phân LTĐH 71, 2 0 cos x dx 7 cos 2x I π + = ∫ 73, 2 0 sin x dx x I π = ∫ 75, 2 0 1 dx 2 sin x I π + = ∫ 77, 2 0 1 dx 2 cos x I π − = ∫ 79, 2 2 3 cos x dx (1 cos x) I π π − = ∫ 81, 2 4 3 2 cos x I c sin x 1 d os x x π π − − = ∫ 83, 2 2 6 1 I x 2 sin x. sin dx π π = + ∫ 85, 2 0 1 sin xI dx π += ∫ 87, 2 2 I x.(2 1 cos2x )sin dx π π = − + ∫ 89, 4 6 6 0 I x cos sin 4x dx si xn π = + ∫ 91, 3 1 dx 2 3sin x I cos x π π + − = ∫ 93, 2 2 0 1 3sin 2x 2 dI xcos x π − += ∫ 72, 2 0 cos x dx cos x 1 I π + = ∫ 74, 2 0 cos x dx 2 cos x I π − = ∫ 76, 3 2 0 cos x dx cos 1 I x π + = ∫ 78, 2 3 6 0 sin x dx cos x I π = ∫ 80, 2 0 1 dx 2cos x si I n x 3 π + + = ∫ 82, 3 8 cot x tan x 2tan2x dx sin 4x I π π − − = ∫ 84, 6 0 1 dx 2sin 3 I x π − = ∫ 86, 2 2 3 0 I cos x 1)c( dxos x π = − ∫ 88, 2 2 0 cos x sin 2x 38 dx sinx co I s x π − − − = ∫ 90, 2 3 0 sin x dx (sinx 3 I cos x) π + = ∫ 92, 6 0 1 dx sinx 3 cos x I π + = ∫ 94, 4 0 cos x sin x dx 3 sin 2x I π − − = ∫ Trang 9 Giải Tích 12- Chuyên đề Tích Phân - LTĐH 95, 2 3 0 sin x dx cos x. sin I x3 π + = ∫ 97, 6 0 tan(x ) 4 dx cos 2x I π π − = ∫ 99, 2 4 0 tan x dx cosx. I cos x1 π + = ∫ 101, 2 0 2 2 3sin x 4cos x dx 3sin I x 4cos x π + + = ∫ 103, 2 4 sin(x ) 4 dx 2sin I x cos x 3 π π π + − = ∫ 105, 2 2 3 cos x dx (1 cos x) I π π − = ∫ 96, 2 0 2 2 I cos x 4sin x sin 2x dx π = + ∫ 98, 2 4 0 I cos sin x dx 5sin x. 2x cos x π = + ∫ 100, 3 6 0 tan dx cos 2x x I π = ∫ 102, 2 3 0 cos 2x dx (cos x si I n x 3) π − + = ∫ 104, 3 4 3 5 4 I x.cos 1 dx s xin π π = ∫ 106, 3 6 cot x dx sin x.sin( I x ) 4 π π π + = ∫ Dạng 4: Tích phân các hàm số siêu việt 1, x ln 2 x 0 1 e I dx 1 e − = + ∫ 3, 2x 1 x 0 e dx e 1 I − − + = ∫ 5, ln 3 x 0 1 dI x e 1+ = ∫ 7, 2 x 1 x 1 e I 1 d − − = ∫ 9, 2x 2 x 0 e dx e 1 I + = ∫ 11, x 1 x 0 e I dx e 1 − − = + ∫ 13, 1 3x 1 0 I e dx + = ∫ 2, ln 2 x 0 e 1dxI −= ∫ 4, 1 x 0 1 dx e 4 I + = ∫ 6, x ln 3 x 3 0 e dx (e 1) I + = ∫ 8, 1 x 0 1 I dx 3 e = + ∫ 10, 1 2x x 0 1 I dx e e = + ∫ 12, x 2 1 2x 0 (1 e ) I dx 1 e + = + ∫ 14, 4 x 1 I e dx= ∫ Trang 10 . Giải Tích 12 CHUYÊN ĐỀ NÂNG CAO Giải Tích 12 * TÍCH PHÂN LUYỆN THI ĐẠI HỌC * * TÍCH PHÂN LUYỆN THI ĐẠI HỌC * Giải Tích 12- Chuyên đề Tích Phân - LTĐH 25,. Giải Tích 12- Chuyên Đề Tích Phân LTĐH *BÀI TẬP LUYỆN THI: Dạng 1: Tích phân các hàm số hữu tỉ 1, 3 2 3 0 I x (1 x) dx= − ∫ 3, 1 2