2 TRẦN QUANG - 01674718379 Genius is one percent inspiration and ninety-nine percent perspiration111... 5 TRẦN QUANG - 01674718379 Genius is one percent inspiration and ninety-nine perce
Trang 11 TRẦN QUANG - 01674718379 Genius is one percent inspiration and ninety-nine percent perspiration
§1 CÔNG THỨC NGUYÊN
HÀM
x x
2 ( x2 x x 3x dx )
x
2 3
1
2
dx x
5 x5 2 x dx
x
7
1
3
7 5 x3 4 x3 2 x3 dx
3 4 5
3
9 ( x 1 )( x4 3 x dx )
10 ( 3 x )( 2 x 1 )2dx
11 x 24 x x x dx
12 x
dx
x
13 x
dx x
2
1
14 x3 2dx
15 x
dx x
2
2
2
4
dx x
17 x x x x
dx x
2
x
dx x
2 2 3
20 x 5dx
21 x 2014dx
3 4
22 x 6dx
23 dx
x
1
24 dx
x
25 dx
x
26
dx x
5 3
27 dx
x
28
dx x
1 3
29 5 x 3 dx
30 x2 2 xdx
31 x 1 x dx2
32 x2 3xdx
33 x
dx x
1 2
34 x4 7x dx3
3
35 x
dx x
2 34 5
36 x
dx
x
32 1
37 x
dx
x
3 23
38 x2 5 x dx3
39 x3 4 5 x dx4
40 2 x2 1 3 x dx3
41 x
dx x
1 56
42
x x dx
2 3
43
x x dx
4
2 3
44
x x ( dx 1)
45
2 4
dx x
46
( 1)(2 x dx x 3)
22
1 1
x
48
2 7 10
dx
49
dx
50
( 1)(2 1) x dx
51
2 2 3 2
52
2 33 2
3x3 2x x22 x dx1
dx x
4 32 4 12 1
dx x
56 sin
sin
x
1 3
57 ( 1 cos 2 x dx )
58 sin x dx
59 sin x sin x dx
2
3
60 cos x dx
5
61 sin x cos x dx
3
62
sin x cosx dx
63 cos xdx2
64 cos xdx4
65 sin xdx5
66 cos5x sin xdx
67 cos sin
x dx x
68 5
sin cos x dx x
69 cos3x sin2xdx
70 cos sin x 3xdx
71 5sin cos x xdx
72 sin2x cos2xdx
73 sin2x cos4xdx
74
cos (x ) sin ( x ) dx
75
sin cos ( )
x dx x
3 2
76 sin cos2 2
dx
77 2sin2
2
x dx
cos2 sin cos
x dx
79 2 sin 3 x cos 2 xdx
80 sin 2 x cos xdx
81 cos 5 x cos 3 xdx
82 sin 2 x cos x dx
2
83
cos x sin x dx
84 cos xsin x dx
5
85 sin dx x , cos dx x
86 tan xdx
87 tan xdx2
88 2
tan cos
xdx x
89 3
cot sin
xdx x
90
tan
sin
2
x dx
x
91 cos x
dx x
92 x2sin( 2 x3 1 ) dx
93 x cos( 3 x2 2 ) dx
94
x
dx
x
2 34 2
95
dx
96 sin
cos
x dx x
1 5
97
x dx x
2
2 3
98 sin
cos
x dx
x
99 tan cos
x dx x
100 tan cos
x dx x
2
101 e2 1xdx
102 e3 4x dx
103
x
dx
e
104
x
x
e dx e
13 3
105
x x
e dx e
1 25 5 2
106 x x
e dx
3 21
107 x x
dx
53 1 4
108 cos x
x e dx
109
cos
x
x
110
x
x dx
2 5
Trang 22 TRẦN QUANG - 01674718379 Genius is one percent inspiration and ninety-nine percent perspiration
111 ln x
dx
x
112
ln
dx
113
( ln )
dx
114 ln
ln
xdx
115 tan ln(cos ) x x dx
116
x
e
dx
x
3
117
tan
cos
x
e
dx
x
118 ecosxsin xdx
119 xe1x2dx
120
ln x
e
dx
x
121
cot
sin
x
e
dx
x
122 cos 2 x e sin cosx xdx
§2 PP TÍCH PHÂN
TỪNG PHẦN
123 x sin xdx
124 ( x2 5)sin xdx
125 x cos xdx
126 x cos2 xdx
127 x sin2 xdx
128 ( x2 2 x 3)cos xdx
129 x2cos2 xdx
130 x2cos2xdx
131 x2 5 x 6 cos 2 xdx
132 x2 4 x 3 cos xdx
133 x 2cos xdx
134 x2 5 x 6 sin 3 xdx
135 sin x dx
136 sin xdx3
137 cos x dx
138 x sin x dx
139 x e dx x
140 4 3 x e 3xdx
x e dx
x e dx
143 x/
x e dx
144 x e dx3 x2
145 ln xdx
146 x xdx ln
147 ln xdx2
148 ln( x2 1) dx
149 x tan2xdx
150 2
ln(cos ) cos x dx x
151 cos x dx2
x
2
sin
x dx x
153 x ln(1 x dx2)
154 x dx 2x
155 x log xdx
156 ln xdx x
157 e dxx
158 ln(ln ) x dx
x
159 sin(ln ) x dx
160 cos(ln ) x dx
161 ex.cos xdx
162 e x(1 tan xtan )2x dx
163 ex.sin2 xdx
ln(1 )2 x dx x
165
ln x dx2
x
166
3 2
1
x dx x
167
ln 2 2 1
1
x
168 ln x 1 x2 dx
169 x ln2 x 1 dx
170 x ln x2 1 dx
171 x ln x dx
x
172 x ln x x
dx x
2
2
1 1
173 x ln x x
dx
2
2
1 1
174
x x ln x dx
1
175
ln( x x ) dx
1
176
ln( x )
dx x
1 3
177
ln x ln x dx
178 x sin cos x 2xdx
§3 TÍCH PHÂN
HÀM VÔ TỈ
179 xdx
dx
x
180 x3 x2 2 dx
181 x
dx x
12
182 ln x ln x
dx x
183
x
dx
e
184
x
x
e
dx
e
1
185 dx
x x
186 dx
x x
x
188 xdx
x
189 x
dx x
34 3 2
dx x
4 3 1
191 x
dx
x
x
193 x2 x 1 dx
194 x dx
x
3 32 6
195 dx
x x
x x
197
x
x
e dx e
198
dx
x x
199 dx
x
200 1 x dx2
201 x dx
x
32 2
202 x2 2 x dx2
203 dx
x
2 1
204 x2 2 x 5 dx
205 x dx
x
22 2
206 dx
x
x x
x x
x x
210 2 x2 1 dx
dx x
1
212 dx
x
213 x dx
x
42 2
214
dx x
215
(1 2 3)
dx x
216
1 1 1 dx x
Trang 33 TRẦN QUANG - 01674718379 Genius is one percent inspiration and ninety-nine percent perspiration
x 1 2 dx
x x
218
1 31 1 dx
x
219
14 dx
220
x dx3
221
( 1) x dx
x x
222
1 1 x dx x x
31
1
x dx
x x
225
3 2
dx
226
2
dx
dx
1
228 x x
dx
2 2
2
dx
22
1
dx
dx
22
2
dx
x x
2 2
dx x
4
234
x dx x x
235
dx
x x x
236
x dx x x
2 3 2 3 1
dx
1
238
dx
x x x
239
dx
x x x
240
dx
x x x
x x x
2
2
249
x dx x
x x
x x
x x
x x
x x
x x
x x
x x
259 x dx
x x
x x
§4 TÍCH PHÂN HÀM
HỬU TỶ
262 x
dx x
2 3 1
263 x x
dx x
33 5 2 1
dx x
4 3 22 3
265 x x x
dx x
6 3 33 21 2
x x
2
dx
2
269 x x
dx x
1
dx
x x
5
3 2
dx
2
dx
dx
dx
x x
5 4
3 2
dx
dx
1 5
x x
2
2
x x
x x
dx
dx
2 2
dx
1 5
x x
x x
x x
dx
dx
dx
2
289 x
dx
2
1
dx
2
2
291 x x
dx
22
1
dx
22
x x x
3 2 2 9 18
294
dx
x x
2 2
1
295
x x x
dx
x x x
4 22
2
296
dx
x x
297
x x x dx
1
298
dx
22
299
dx
x x
300
x
dx
301
dx
x x x
22
1 1
x x x
Trang 44 TRẦN QUANG - 01674718379 Genius is one percent inspiration and ninety-nine percent perspiration
x x x
3 6 2 11 6
3 2 4 4
305
x x
2
1
1
306 x dx
3
308 ( x ) dx
x dx
4
310 x dx
5
311
x dx
x
2
2
x
x x dx
x
314
x x dx
2
x
1
1
316
x x dx
4
1
317 x
dx
x
3
1
318 x
dx
x
3
2
1
319
22
1
3
dx
2
dx
x x x
3 22
4 3
6 3 2 1
322 xdx
x
4 1
323 x
dx x
24
1 1
324 x
dx x
24
1 1
325 x
dx
x
421
326 dx
x
4 1
327 x dx
x
44 1
x x
x x
x x
331 x dx
1
332 x dx
1
333 x
dx
x
6 21
334 x
dx
x
6 21
335 x
dx
x
336 x
dx
x
6 31
337 x
dx
x
6 41
338 x
dx x
46
1 1
339 x
dx x
46
1 1
340 dx
x
6 1
341 x x
dx x
26 1
342
x
dx x
1012
5 2
x
dx x
1
x
dx x
10199
345
x dx x
346
x dx x
347
x dx x
348
dx
x x x x
349
dx
x x x x
x x
4 10 2 9
x x
352
dx
353
x x x dx
354
x x x dx
355 dx
x x
5 20
356 dx
x x
9 7 5
357 dx
x x
7 13
358 dx
x x
359
dx
x x x
360 dx
x
4 1
x x
3 100 5
362
x x
363
x dx x
19 10 2 2
364 x dx
x
44 1
20102010
1 1
§5 TÍCH PHÂN HÀM
LƯỢNG GIÁC
366 sin22 xdx
367 cos2x sin4xdx
368 sin 3 x cos xdx
369
sin sin
dx
x x
370 sin cos x 2 x cos 5 xdx
371 sin cos tan cot
dx
372 sin sin sin sin
xdx
3 4 36 3 2
373 cos3x cos 3 xdx
374 cos2x cos 2 xdx
375 sin 4x cos 4xsin 6x cos 6x dx
376 sin cos x 2 xdx
377 sin 3 x cos xdx
378 2 sin 2x sin cosx x cos 2x dx
379 sin3 x dx
2
380 cos
x dx
x x
381 sin cos
x dx x
382
dx
x x
383
cos
dx x
384
sin cos
dx
385 sin
cos
x dx x
1 4 3
386 sin cos
x dx
x
387
cos sin
dx
388 sin2 2x sin2x dx
389 sin
cos
x dx
x
2 4 4 1
390 cos sin
x dx x
391
sin cos
dx
392 sin
cos
x dx x
393 sin cos
cos
dx x
394 sin
cos
x dx x
395 cos
cos
x dx x
396 cos 4 x cos2xdx
397 1 cos3x.sin cosx 5xdx
398 sin cosx x cosx dx2
1
399 cos
cos sin
x dx
x x
1 2
400 cos 2xsin 4x cos 4x dx
401 sin
cos
x dx x
402 cos3xsin3x dx
403 sin sin
sin
dx x
Trang 55 TRẦN QUANG - 01674718379 Genius is one percent inspiration and ninety-nine percent perspiration
404 sin 4x sin 2x cos 2x 3dx
405 tan
cos
x
dx x
406
dx
407 sin cos
dx
408 sin cos
cos
dx x
409 tanx e 2 sinxcosxdx
410 esinxcosxcosxdx
411 sin xcosx cosx dx2
412 sin
cos
x
dx x
1 3 2
413 cos4xsin6xcos6x dx
414 cos
sin
x
dx
x
415 sin cos
cos
dx x
416 sin
cos
x
dx x
1 4 34
417 sin sin
cos
dx x
418
tan tanx x sinxdx
1
2
419 cos3x1cos2xdx
420 cos sin cos
sin
dx x
2
421 sin sin
cos
dx x
1 3 33
422 tan32 xdx
423 tan x tan3x dx
424
cos
dx
x
425
cos sin
dx
426
sin cos
dx
3 5
427
sin sin cos cos
dx
2 2 5 3 2
428
cos sin
dx
3
429 cot xdx4
430 tan ln cos x x dx
tan cos
x dx x
1 1
432 cos sin
x dx x
433
sin
dx x
434 cos sin sin cos
dx
435 cos
sin
x dx x
1 2 2
436
sincoscos
x dx
x x
2
437 sin cos cos sin
dx
438 sin cos
x dx
x
439
cos x sin x dx
1
440
sin cos
dx
2
441
dx
442
dx
443
dx
444 cot3x cot x dx
445 cos sin
dx
2 2 3 3 1
446
sin
dx
x
447 sin cos sin
x dx
2 4
sin cos cos
x
dx
2
sin cos
x dx
450
sin sin cos
x dx
x x
4
451 sin cos cos sin
dx
452 sin cos sin cos
dx
453 sin
sin cos
x dx
x x
2 3
454
cos cos sin
x dx
x x
4
455
sin
tan cos sin
x
dx
4
456
sin sin
dx
x x
4
457
cos sin
dx
x x
6
458
sin sin
dx
x x
6
459
dx
460
sin cos
dx
x x
461
sin cos
dx
x x
462
sin cos
dx
x x
463
sin cos
dx
x x
464 sin cos cos sin
dx
465
cossin sincos
dx
466 cos sin cos sin
dx
467 cos sin cos sin
dx
468
cossin sincos
dx
469 sin sin cos
x
dx
2 5 2 1
470 sin cos
dx
2 3 2 2
471
coscos sinsin
dx
472 sin sin cos
x dx
x x
473 cos
x dx
474 sin cos
dx
§6 NGUYÊN HÀM
PHỤ
475
sin sin cos x dx
476
sin cos cos x dx
477
sin sin cos x dx
478
sin cos cos x dx
479
sin4sin4cos x 4 dx
480
sin4cos4cos x 4 dx
481 2sin sin22x xdx
482 2cos sin22x xdx
483
xex xdx
e e
484
xe x xdx
e e
485
xex xdx
e e
486
xe x xdx
e e
Trang 66 TRẦN QUANG – 01674718379 Reading without reflecting is like eating without digesting
§7: CÔNG THỨC
TÍNH TÍCH PHÂN
1 ( x x x x dx )
2 3 2
1
2
x
5 3 5
3
3
1
x
2
5
4
0 2
1
2
4 x dx 2
x
dx x
2
3 3 2
2
2
3
1
e
0
( x 1)(x x 1)dx
1
( x x x x dx )
9 4 x 3x 4x dx
3
7 2
3
5
2
x x x dx
x
11
2
1
x
3
3 2 1
2 x 3 3 x dx
13
2
1
1
x dx
14
5
2
dx
x 2 x 2
15 02
2
1 xdx dx
x
16
2
2
3
1
x dx
x
17 04x x2 9 dx
18 1 0
19 ) 1
x
19 1
0
3 2 3 ) 1
x
20 1
0 2 5
1 dx
x x
21 1
0 2x 1
xdx
22
1
2 0
1
x x dx
23
1
0
1
x x dx
24 23
5 x x2 4
dx
25 3
3 5 1
2
dx x
x x
26 2
1
0 1 x2
dx
27 1
2
4 x
dx x
28 2 1
2
2 4 x dx
29 3
0 2 3
x dx
0
2 2
) 2 )(
1
dx
31 1
0
2 4
1
x x xdx
32
0 2
dx
33 2
1 3
2 1
dx x x
34
1
0 1 x2 5
dx
35
2/ 3
2
dx
x x
36
2 2 2
2
x dx x
37
2
2 0
2
x x x dx
38
1 0
dx
39
2 2 1
( 1).
ln
40
2 1 0
4 2
x x
e
41 0ln2
1
x
xe dx
e
42 12ex(1 e x) dx
x
43 01
2
x x
e dx
44 0/2 cose xsin xdx
45
0
) 6 2 sin( x dx
/2
/3
(2sinx 3cosx x dx)
47 /6
0
sin3 x cos2 x dx
48 /4 2
0
tan cos
x dx x
49 /3 2
/4
3tan x dx
/6
(2cot x 5) dx
51
/2
0 1 sin
dx x
/2
0
1 cos
1 cos x dx
x
0
sin cos x xdx
54
/6
(tan x cot ) x dx
55
/2
/2
sin( ) 4 sin( 4 )
x dx x
56 /4 4
0
cos x dx
57 14
x
e dx x
58 1e 1 ln x dx
x
59 1eln x dx
x
60 01xe dxx2
61
1 0
1
1 exdx
62
ln2
0 1
x x
e dx e
63
ln3
3
x
x
e dx
e
64 e x x dx
ln 2
x
x x
1
ln ln 3 1
2
0
2 4
x dx
67
/
cos sin sin
2
0 1
dx x
sin cos
6
0
2 2
x dx
§8: PP TÍCH PHÂN
TỪNG PHẦN
69
/
sin
4
0
2
70
/ ( sin ) cos
2
2 0
71
/4
0 (1 sin2 )
72
/ cos
3 2 0
73
/
/ ( x )sin xdx
4
6
74
/2
2 0
(2 1)cos
75
/2
0 ( 1)sin2
0
x cos xdx
77
1 0
cos x dx
78
1 0
sin x dx
79 2/2
0
sin
Trang 77 TRẦN QUANG – 01674718379 Reading without reflecting is like eating without digesting
80 2/2
0
cos
x x dx
81
2/4
0
cos
82
2
0
sin
83 /3
2
0
1 sin
cos
x
84 /4 2
0
tan
85
/4
0 1 cos2
x
86 /3 2
/4
tan
87 1
0
2
)
2
( x e xdx
88 xexdx
2
ln
0
89 x x dx
e
1
ln
90
2
1
( x 2)ln xdx
1
ln
e
92
2
3
1
ln x
dx
x
93 3
2
2
)
ln( x x dx
94
/2
3
0
sin5
x
95
/2
cos
0
sin 2
x
96 e xdx
1
3
ln
e
1
2
3
ln
1/
ln
e
e
x dx x
99 22 1
ln e
x dx x
4ln( )
1
9 x dx x
101
3
2 1
3 ln ( 1)
x dx x
102
1
3
2 ln
e
x
103
2
1
1 ln
e
x
xdx x
104 /3 2
/6
ln(sin ) cos x dx x
105
2 1
cos(ln ) x dx
106
3
2 1
1 ln( x 1)
dx x
107 x ( e x x 1 ) dx
0
1
3 2
1 3 0
x
x e dx
109
4 x 1
110
/4 3 0
sin 4
x
111
/ cos sin 2
0
2
x
112 1
2
2
x
113 / tan ln(cos )
cos 4
0
dx x
114
/
sin
2
0
x
115 2
0
2
dx
xe x
116 1 0
dx
xe x
117 /2( cos ) cos
0
x
118 /2 2 1 0
sin2 x e x dx
1
1 ln
e
xdx x
120 e2ln ln(ln )
e
x
121
e
dx x x
x x
1
2
ln 1 ln ln
122
3
2
ln(ln )
e
e
x dx x
123
1 0
ln( 1) 1
x dx x
1
ln 1 ln
dx x
1
( 1)ln
ln
e
dx
x x x
126 2
2 1
ln
127 2 1
ln
x
x e ex
x
1
1 3 2ln ln
1 2 ln
dx
129 /
ln(sin cos ) cos
4
2 0
dx x
1
( 1)ln
ln 1
e
dx
x x
1
3
x x
dx x
132
0 sin x
e xdx
133 /2
0
2cos cos 2
x x e dx
134 /2 2
0
sin cos
x
1 2 0
ln(1 ) 1
x dx x
1
137 2
1
0 (2 x x 1) ex x dx
§9: TÍCH PHÂN
CÓ DẤU TRỊ TUYỆT ĐỐI
138 3 x dx
1
5 2 1
2
1 2 3 2
141 2 2
0
1
142
2 3 1
2
143 5 3 2 2
144 5 3 2 2
145
2 2
1 3
x
4 2 0
3
x
147
4 2
( x 1 x 3) dx
148
2 1
( x 2 x dx )
149
1 2
(2x 3 3x 4)dx
150 1
0
( x 5 x 6 ) dx
151
4 2 1
x x dx
0
2 3
4
4 x x dx x
153
1 1
4 x dx
154 3 /2
0
sin x dx
155 2 /3
0
cos x dx
156 /2
0
cos2x dx
0
sin 2
3
158
0
1 sin2 x dx
159 2 0
2 cos
160 3 /4
0
sin x cos x dx
161
0
cos x sin xdx
162 1 sin xdx
Trang 88 TRẦN QUANG – 01674718379 Reading without reflecting is like eating without digesting
163
0
1 cos2xdx
164
0
1 cos xdx
165
0
1 sin xdx
/6 tan x cot x 2dx
167
/2
cos cosx x cos xdx
168
3
0
2x 4 dx
169 2
0
3x x 4 dx
170 3
1
3x 4x 5x dx
1
ln 1
e
x dx
172 2
0
ln x x 1 dx
§10: TÍCH PHÂN
CÓ CẬN ĐẶC
BIỆT
173
/4 7 5 43
/4
1 cos
x x x x dx
x
174
/2
cos ln(x x 1 x dx)
175
1/2 1/2
1 cos ln
1
x
x
2 1
177
1
x dx
178 1 42 1
sin 1
x
179
/2 5
/2
sin
1 cos x dx
x
180
/2 2
/24 sin
xdx x
181
/2 2
/2
cos
4 sin
x
182
12 1xx dx
183
1
1
1 2 x dxx
184
1
2
dx
185
2
sin
3 1x xdx
186
3
3
2 2 1
1
dx
x
x
187
1
2
1(4 1)(x 1)
dx x
188
/2
sin sin3 cos5
x x x dx e
189
/2
6 1x
190
/2 2 2
/2
sin
1 2x
191
/2
0
cos cos sin
n
x dx
192
0
sin sin cos
x dx
193
/2
0
sin
x dx
194
/2 2009 2009 2009 0
sin sin cos
x dx
195
0
cos cos sin
x dx
196
/2 4 4 4
0
sin
x dx
0
.sin
4 cos
x x dx x
0
cos
4 sin
x
/2
0
1 sin ln
1 cos x dx x
200 /4
0
ln(1 tan ) x dx
201
2
3 0
.cos
0
.sin
203
01 sin
x dx x
204
0
sin
2 cos
x x dx x
0
sin
1 cos
x x dx x
0
sin4 ln(1 tan )x x dx
0
sin
9 4cos
x
0
sin cos
209
/2
0
sin sin cos
x dx
210
/2
0
cos sin cos
x dx
211
/2
0
sin sin cos
x dx
212
/2
0
cos sin cos
x dx
213
0
sin
x dx
214
0
cos
x dx
215
0
sin
x dx
216
0
cos
x dx
217 /2 2 0
2sin sin2 x xdx
218 /2 2 0
2cos sin2 x xdx
219
1 1
x
e e
220
1 1
x
221
1 1
x
e e
222
1 1
x
§11 TÍCH PHÂN
HÀM HỬU TỈ
223 3
1 3
x x dx
224 1
0 2
6
5x
x dx
225
2
x dx
x x
226
2
1
dx
x x
227
1
3
xdx
x
228
4
3 4
x x ( dx )
229
x x
x dx
3 7 7 1
1 1
231
x x
232 3
0 2 3 1
2x
x
dx x
233
1
0
3 2
x
234
3
2
9 2
1 x
dx x
235 4
1
2( 1 x )
x dx
236
dx
x x
4 2
0 2
6 5
11 4
x x
dx x
238 1 3 0
1 1
x
Trang 99 TRẦN QUANG – 01674718379 Reading without reflecting is like eating without digesting
239 0 3 2
2
1
x x
240
3
2
241
3
0(3 1)
x
3
0
2
2
1
2
3
dx x
x
243 2
0
2
2
3
4
9 4 2
dx x
x x
x
244 1
0
1
( x 2) ( x 3) dx
245 1 3 2
0
1 1
x
246
1
4
01 x dx
x
247
2
4
1
1
(1 ) dx
x x
2014
1
1
249
x
250
2
2
0
1
4 x dx
251
4
1
1
1 x dx
x
252
2
0
2
1 x dx
x
253
4
1
1
1 x dx
x
254
3
1
1 x dx
x x
255
6
0
1
1 x dx
x
256
4
x
x x
1 4 2
258
x dx x
259 1 0
6
4 5 6
1
2
dx x
x x x
260 3
2 3 2
2 3
3 3 3
dx x
x
x x
261 1 5 /2 2
4 2 1
1 1
x
dx
x x
262 1
0
1
dx (x 4x 3)
§12 TÍCH PHÂN
HÀM LƯỢNG GIÁC
263
/
sin cos
4
0
2x xdx
264
/
tan
4
0
xdx
265
/
sin cos
2
0 1 3
x dx x
266
/
sin
2 3 0
xdx
267 x dx
0
2 sin
268
0
2 3 cos x
0
1 2sin
1 sin2
x dx x
0
sin cos x xdx
271
/
sin cos
2
0
0
sin cos x xdx
273 /2 3 3
0
(sin x cos ) x dx
274
/2 3
0
cos cos x dx 1
x
275
/
sin cos cos
2
0
2 1
dx x
276 /4 3 0
tan xdx
277 /3 4
/4
tan xdx
278
/3 3
/4sin cos
dx
279
/2 3 2
0
sin
1 cos x dx
x
280
/2 3
0
cos
1 cos x dx
x
281
/3 4 /6sin cos
dx
282 /
/
sin cos 2
6
dx
283 /
/
tan
3
2
x dx
0
cos2 (sinx x cos )x dx
(tan cos )
4 0
x
286
/4 2 32 5 0
sin (tan 1) cos
287
/3 2 2 /3
1 sin x 9cos x dx
288 /2
/3
1 sin x dx
289
/2
0 2 cos
dx x
290
/2
0
1
2 sin x dx
291
/2
0
cos
1 cos x dx
x
292
/2
0
cos
2 cos x dx
x
293
/2
0
sin
2 sin x dx x
294
/2
0
1 sin x cos x 1 dx
295
/2
/2
sin cos 1 sin 2cos 3
x x dx
296
/4
4
dx
0
(1 sin )cos (1 sin )(2 cos )
298
/3
/4sin cos( )
4
dx
299
/3
/6sin sin( )
6
dx
300
/2
0
cos
7 cos2
xdx x
0
sin cosx x cos xdx
302
/2 2
0
cos
2 cos
xdx x
/26 3 5 0
1 cos sin cosx x xdx
/2
0
sin2 sin
1 3cos
x x dx x
Trang 1010 TRẦN QUANG – 01674718379 Reading without reflecting is like eating without digesting
305
/3
0
cos
2 cos2
xdx
x
306
/2 2
0
cos
1 cos
xdx
x
307
/3 2
/4
tan
cos 1 cos
308
2
0
sin2 cos
1 cos
dx x
309 4
0
sin ( 1)cos
sin cos
dx
0
cos x 1 cos xdx
311 4
0
sin
4 sin2 2(1 sin cos )
x dx
312 /6 4
0
tan
cos2
x
dx
x
sin cos
2
0
2
4
x
dx
sin cos
2
0
2
x
dx
§13 TÍCH PHÂN
HÀM VÔ TỈ
315 22 0
2 1dx
x x
316 1
3
1 dx
x x x
317 1
dx
318 2
11 x 1 dx
319
6
dx
x x
320 2
0 5
4
1 dx
x x
321
10
dx
x x
0
2 3
1dx
x x
323 1
3 4
dx x x
324 3
7
0
33 1
1
dx x x
325
2 3
2
dx
x x
326
2
x x dx x
327
2 2 0
1
1 xdx x
328
2 3 2
dx
x x
329
2 3
dx
x x
330
1
0
1
x x dx
331
1
1 1
x x
332
1
2 3
dx x
333 2 2
1
2014
334
3
0
10
x x dx
335
1
2 0
1 x dx
336
1
2
dx
337
2 2
dx x
338
2
x dx
x x
339
2 2
2 3
dx x
340
2 2 2
2
x dx x
341
5
1
12 x 4 x 8 dx
342
ln3
dx
e
343
ln2 2
x x
e dx
e
344
1
1 3ln ln
e
x x dx x
345
ln2
ln
ln x dx 1
x x
1
x e x dx
347
ln2
3
x x
e dx
e
348 ln3
x
e e
349
1 0
x
e e
350
ln2 0
1
x
e dx
351 1
01 x
x
e
dx e
352 ln2
0 x 5
e dx
353
1 0
1 4
x dx
e
354 ln8
3
ln e 1 dx
e
x x
355 ln 8 3 ln
2 .
1 e dx
356 ln2
0 1
1
dx e
e
x x
357
2 1
1
1 ex dx
358
x x
e dx
e
359
1
x x
e
1
ln (ln 1)
361
x x
e
362
ln3 0
1 1
x dx
e