-
Created by T. Madas
Created by T. Madas
INTEGRATION
MIX
-
Created by T. Madas
Created by T. Madas
1. ( )126 4 3x dx+
2. 12
3 1dx
x +
3. 12
4 1
xdx
x −
4. 12
4 1dx
x +
5. 12
4 1
xdx
x +
6. ( )2
sin cosx x dx+
7. ( )2
2sin cosecx x dx+
8. ( )( )
5
3 1 2 1dx
x x− +
9. 4 sin 2x x dx
10. 7
4dx
x
11. 2
2x dx
x
+
12. ( )
72
10
1 4dx
x−
13. ( )1 2cos sinx x dx+
-
Created by T. Madas
Created by T. Madas
14. ( )2 12cos cos 2x x dx−
15. 2
14
4
xdx
x −
16. 2
9
2 1dx
x x+ −
17. ( ) 28 1 e xx dx−+
18. ( )2
2e ex x dx−+
19. ( )
3
6
3 2dx
x +
20. ( )
3
6
3 2
xdx
x +
21. ( )sin 2cos sinx x x dx−
22. ( )2 cos sin 2
2cos
x xdx
x
+=
23. 8 3
4
xdx
x
−
24. 2
3
6
8
xdx
x +
25. ( )3
1 2cos sinx x dx+
26. cos x dx
-
Created by T. Madas
Created by T. Madas
27. 3
2 1dx
x −
28. ( )
6
10
2 1dx
x +
29. ( )( )
3 1
2 1 2
xdx
x x
−
+ −
30. ( )2
2 sin x dx+
31. ( )145 2 3x dx−
32. 4
3
e 3
e
x
xdx
+
33. 5e xx dx
34. 3
42
xdx
x +
35. ( )( )
2
2 4dx
x x− −
36. 3
4 1dx
x +
37. 2
11 dx
x
+
38.
( )3
2 1
xdx
x −
-
Created by T. Madas
Created by T. Madas
39. cos sinx x dx−
40. sin cosx x dx−
41. ( )sin 4 3x dx+
42. 1
xdx
x +
43. ( )cos 5 2x dx−
44. 3sin 2x dx
45. ( )21 sec sinx x dx+
46. ( )2
1 2cos x dx−
47. ( )2 21 cot secx x dx+
48. 2 cos3x x dx
49. ( )( )
3
2 1dx
x x+ −
50. ( )4
10 3 1x dx+
51. ( )126 2 1x dx+
-
Created by T. Madas
Created by T. Madas
52. 2 2
1
cos tandx
x x
53. cos sinx x dx
54. 2
2
cosdx
x
55. 22 2tan x dx+
56. 2
1 cos
sin
xdx
x
+
57. ( )
2
2
1 cos
sin
xdx
x
+
58. sin 3x x dx
59. ( )
3
2
2 1
xdx
x +
60. ( )1
4 5x dx−
−
61. 1
4dx
x
62. ( )( )
1
1 2dx
x x+ +
63. 1x
dxx
+
64. 1
xdx
x +
-
Created by T. Madas
Created by T. Madas
65. 2
4
1 2
xdx
x−
66. 2
1
9 1
xdx
x
+
−
67. sin 4x x dx
68. ln x dx
69. ( )
2
4
2 7dx
x −
70. 24cos x dx
71. ( )2 21 tan secx x dx+
72. ( ) 21 tan secx x dx+
73. ( )2cosec 3 1x dx+
74. ( )212sec 2 3x dx+
75. sin x
dxx
76. 2 26e x dx+
77. ( )2 21 cot secx x dx−
-
Created by T. Madas
Created by T. Madas
78. sin cos
sin cos
x xdx
x x
−
+
79. sec tan 1 secx x x dx+
80. tan 2 sec2x x dx
81. 2 lnx x dx
82. 2
6
2 8dx
x x− −
83. 23cot x dx
84. cos 2 sinx x dx
85. 2
4xdx
x
+
86. ( )527 2 3x dx−
87. 2
34
xdx
x−
88. ( )1sin 2x x dx
89. 2
4
4 4 1dx
x x+ +
90. 3
4 1dx
x +
-
Created by T. Madas
Created by T. Madas
91. 1
xdx
x −
92. ( )
12
1
3 2dx
x −
93. 6 3
2
xdx
x
+
94. 4 1
2 5
xdx
x
+
−
95. 2
4
1
xdx
x −
96. 2
2 1
xdx
x −
97. 4
2
1 cos
cos
xdx
x
+
98. ( )( )
2
17 5
2 3 2
xdx
x x
−
+ −
99. ( )sin 2 1x x dx−
100. ( )3
4 3 2x dx−
101. x x dx
102. 53
32 2
1 35
dx x C
x x
−= − +
-
Created by T. Madas
Created by T. Madas
103. 3
2 4dx
x−
104. 1
1 cos2dx
x+
105. 2
2
2dx
x x−
106. 2
ln xdx
x
107. 2
3
3
1
xdx
x +
108. 2 1
2 1
xdx
x
+
−
109. ( )( )
14 1
1 2 1
xdx
x x
+
− +
110. 6
2 3
xdx
x +
111. 4 2
2
sin cos
sin
x xdx
x
+
112. ( )
2
4dx
x x−
113. 1
2 1dx
x+ −
114. 4
6 1dx
x −
115. 2
2
3e
e 1
x
xdx
−
-
Created by T. Madas
Created by T. Madas
116. 2secx x dx
117. cosec2 cot 2x x dx
118. 2 2tan secx x dx
119. sin 2 cosecx x dx
120. ( )2
2cos 3sinx x dx−
121. sin tan
cos
x xdx
x
+
122. 2
1 sin
cos
xdx
x
+
123. sine cosx x dx
124. 2 sinx x dx
125. ( )3
2 1x dx+
126. 4
2
tan
cos
xdx
x
127. ( )( )
2
2
4 6 5
2 2 1
x xdx
x x
− +
− −
-
Created by T. Madas
Created by T. Madas
128. 3 1
2 3
xdx
x
−
+
129. 28
1 2
xdx
x−
130. ( )
32
10
3 1dx
x +
131. 5x dx
132. 2sin cosx x dx
133. ( ) ( )22 1 sin 1x x x dx+ + +
134. ( )( )22 1 1x x x dx+ + +
135. ( ) ( )21 cos 2 1x x x dx+ + +
136. 1
2dx
x+
137. 1
e e 2x xdx
−+ +
138. ( )2 3tan 1x x dx+
139. ( )3 2ln 1x x dx+
140. 2 2sin secx x dx
-
Created by T. Madas
Created by T. Madas
141. 23sec sinx x dx
142. ( )
3
1
1 lndx
x x+
143. 3 lnx x dx
144. ( )3ln 2x x dx
145. 44 cos sinx x dx−
146. 3
cos
sin
xdx
x
147. 24sec
tan
xdx
x
148. 2sec tan 1 tanx x x dx+
149. 2
1 2tan
cos
xdx
x
+
150. 2tan x dx
151. ( )
2
2
1 sin
cos
xdx
x
+
152. 2cos
1 sin
xdx
x+
153. 1
1 cosdx
x+
-
Created by T. Madas
Created by T. Madas
154. cos
sin
xdx
x
155. 52
410
2 1
xdx
x +
156. sin x dx
157. 2
1 2
xdx
x−
158. ( )
5
12
1 2dx
x−
159. 4
5 2
2
5 8
x xdx
x x
+
+ +
160. 1
xdx
x −
161. ( )
1
1dx
x x+
162. 3
4
2 1
2
xdx
x x
+
+
163. ( )
2
1
xdx
x x
+
+
164. ( )sin ln secx x dx
165. ( )
2
2
1 2cos
3sin
xdx
x
+
-
Created by T. Madas
Created by T. Madas
166. 1
lndx
x x
167. ( )2
2 3x dx−
−
168. 2 12sec sin 22
x x dx+
169. ln x
dxx
170. 4cos
sin
xdx
x
171. 2 26 tan secx x dx−
172. 4 26cos 2sinx x dx−
173. sin 4 cos4x x dx
174. 1
cosec cotdx
x x−
175. 2
1
xdx
x −
176. 23e
e 1
x
xdx
−
177.
( ) 3 231
2dx
x x+
178. 7
4
4
1
xdx
x +
-
Created by T. Madas
Created by T. Madas
179. 29 1
xdx
x +
180. 3
2dx
x x+
181. 3
1
xdx
x+
182. 23 2
4 1
xdx
x
+
+
183. 2 3
3 4 2dx
x x x+ −
184. 22sin 2 cosx x dx
185. ( )( )
2
2
10 23 11
2 3 2 1
x xdx
x x
− +
− −
186. sec
sec tan
xdx
x x−
187. cos6x x dx
188. sin sin3x x dx
189. 14cos3 sin32
x x dx+
190. 2sin 6x dx
191. 2
cos2
1 cos 2
xdx
x−
-
Created by T. Madas
Created by T. Madas
192. 2 2
1
cos tandx
x x
193. 33cos 3x dx
194. 43sec x dx
195. 2sin cos3x x dx
196. 2sin
cos sin
xdx
x x+
197. 4 1
2 1 3 4dx
x x+
− −
198. 2 sin3x x dx
199. 2cosec 2x dx
200. 3sin 2 cos2x x dx
201. 2cot 3x dx
202. 7
3dx
x
203. sin cos
1 cos2
x xdx
x−
204. sin cos
1 cos2
x xdx
x+
-
Created by T. Madas
Created by T. Madas
205. ( )5
4 3 2x dx−
206. 1 sin
cos
xdx
x
+
207. sin 2 secx x dx
208. sin 2 sinx x dx
209. 2cosx x dx
210. ( )13sin 1x dx+
211. 2
1 ln xdx
x
−
212. 234 e
xx dx
−
213. ( )2
ex x dx+
214. 4
2
e e
e
x x
xdx
−−
215. lne x
dxx
216. ( )
4
1
2 3 1dx
x +
217. ( )cos ln x
dxx
-
Created by T. Madas
Created by T. Madas
218.
2
2
2
2
4 e
1 2e
x
x
xdx
+
219. ( )
4
3 2 1dx
x +
220. 2
1
cos tandx
x x
221. sin 2
1 cos
xdx
x+
222. 3sin x dx
223. 1 1sin 2 cos33 2
x x dx−
224. 2
3
4 2
xdx
x−
225. 2
1
sin cosdx
x x
226. 2
3
4 2
xdx
x−
227. ( )
32
1 4
4 ln
xdx
x x x
−
−
228. 4
sin
cos
xdx
x
229. 2cosec
1 cot
xdx
x+
230. ( )2 1cos 4x x dx
-
Created by T. Madas
Created by T. Madas
231. ( )( )
3
2 1dx
x x− +
232. ( )( )
1
2 2dx
x x− +
233. 4 3
2 1
xdx
x
−
+
234. 1
1 x dxx
+
235. sec
cos sin
xdx
x x−
236. 2
2
2
1
xdx
x
−
−
237. 3 2
1dx
x x−
238. 32
26
2 1
xdx
x −
239. 1
1 1dx
x+ −
240. 1
5
xdx
x
+
−
241. ( )
22
3
xdx
x
+
242. 2 14e sin33
xx dx
−−
-
Created by T. Madas
Created by T. Madas
243. 22 sec 2x x dx
244. 8cos sinx x dx
245. 5
7
sin
cos
xdx
x
246. tan3x dx
247. 1
sec 1dx
x −
248. 2
4
sin
cos
xdx
x
249. sin cos
1 cos
x xdx
x−
250. ( )
14 1
4
xdx
−−
251. 2e 2e
e 1
x x
xdx
−
+
252. 22 3 2
1
x xdx
x
− +
−
253. 21 cot x dx−
254. 2
4 2
1xdx
x x
+
−
255. 4cosec x dx
-
Created by T. Madas
Created by T. Madas
256. 122 e
xx dx
257. ( )2
e 2ex x dx−+
258. ( )e sin ex x dx
259. 2ex dx
260. ( )2
2cos 3x dx−
261. 2
2
xdx
x −
262. ( )
1
3
1 e xxdx
x
+
263. 4 1x
dxx
+
264.
( )322
1
1
dx
x−
265. 2
2 1
x
xdx
+
266. ( )2 1 2 3x x dx− −
267. 5
3
9
1
xdx
x +
-
Created by T. Madas
Created by T. Madas
268. ( )2
3sin cosx x dx−
269. 2
4
10
xdx
x −
270. 3
3
4e
1 e
x
xdx
−
271. ( )1 cos sin cosx x x dx−
272. ( )2
tan 1x dx−
273. 1 e
1 e
x
xdx
+
−
274. 4sin 2 cos 2x x dx
275. 1
sin cosdx
x x
276. 2
1
sin cosdx
x x
277. 1
1 sindx
x−
278. 1
e 1xdx
+
279. ( )1 sin sin 2x x dx+
280. sec tanx x x dx
-
Created by T. Madas
Created by T. Madas
281. sin3 cos2x x dx
282. ( )
2
1 2
2 ln
xdx
x x x
−
−
283. 142 e
xx dx
−
284. 4
4
xdx
x
+
−
285. ( )322 33 4 2x x dx−
286. 1x x dx+
287. 3 2
1
2 3
xdx
x x
+
+ +
288. sin 2 cosx x dx
289. sin 2 cos2x x dx
290. 3
3 1
x
xdx
+
291. tan
tan sec
xdx
x x−
292. ( )
2ln x
dxx
-
Created by T. Madas
Created by T. Madas
293. ( )
( )( )
2
2
8 1
3 1
x
dx
x x
+
− +
294. 31
x dxx
295. ( )( )4
21 2 1x x x dx+ + −
296. 4sin cosx x dx
297. 2
2 6
6 1
xdx
x x
+
+ +
298. ( )
1
4dx
x x −
299. tan
1 cos2
xdx
x+
300. 2 2cos sinx x dx
301. 3
2
3 5
1
x xdx
x
+
+
302. 2sin 2x dx
303. 2
cos2
cos
xdx
x
304. 3sec tanx x dx
305. ( )2
ln 1x x dx −
-
Created by T. Madas
Created by T. Madas
306. 2
3 5
xdx
x +
307. 2 1
3 1
xdx
x
+
−
308. ( )4
23x x dx+
309. 2 2
9
9dx
x x−
310. 3
cos
sin
xdx
x
311. 3
1 2
xdx
x
−
+ −
312. 2
4
4
xdx
x
−
−
313. 2sin
cos sin
xdx
x x+
314. ( )2
21 x dx−−
315. 2
tan
cos
xdx
x
316. ( )2
3sin cosx x dx+
317. ( )
2
3
sec
1 tan
xdx
x+
318. 2 2
1
cos sindx
x x
-
Created by T. Madas
Created by T. Madas
319. cot 2x dx
320. 2x dx
321. sin sin cos
1 cos
x x xdx
x
+
−
322. 4
1
cosdx
x
323. sin cos
1 cos2
x xdx
x+
324. 2ln x
dxx
325. ( )2 1sin cos 2x x dx
326. 3e 1
e 1
x
xdx
+
+
327. 1
xdx
x −
328. 2 3x x dx
329. 2 13 x dx+
330.
32
52
2 1
2
xdx
x x
+
+
331. ( )
1
1dx
x x+
-
Created by T. Madas
Created by T. Madas
332. 1
xdx
x −
333. ( )2
1
1dx
x x+
334. 4sin sin 2x x dx
335. ( )2
tan cotx x dx+
336. 2
2
2 2
2 2
x xdx
x x
+ −
− +
337. sin cosx x x dx
338. 3sec tanx x dx
339. 1
cosec cotdx
x x−
340.
14
54
2 1
4 4
xdx
x x
+
+
341. ( )ln 1x
dxx
−
342. eex
xdx
+
343.
( )2
1
1
dx
x x+
-
Created by T. Madas
Created by T. Madas
344. 2 e xx dx−
345. e x
dxx
346. e xx dx
347. ( )( )
24 1
1 2 1
x xdx
x x
− +
− −
348. e cosx x dx
349. 2
2
5
5 3
x
xdx
+
350. 5
3
3
1
xdx
x −
351. 2
2
4 2
xdx
x x
−
− −
352. ( ) 2
1
1 1dx
x x− −
353. 3 2
2
3 10 3
3
x x xdx
x
− + −
+
354.
( )322
4
4
dx
x+
355. ( )
2
2
1
1
xdx
x
+
+
-
Created by T. Madas
Created by T. Madas
356. 2
cos tan
1 tan
x xdx
x
+
+
357. 1 x
dxx
+
358. 3 4
4
4 1
1 1
x xdx
x
+
+ +
359. ( )2
ln x dx
360. 18cos sin 2x x dx
361. 5 2
1dx
x x+
362. ( )22sin cos 1x x dx+ −
363. ( )sin cosx x x dx+
364. 1
2 3
1 1e x dx
x x
+
365. 4sec
tan
xdx
x
366. ( )
3
cos
cos sin
xdx
x x+
367. 2
20
4
xdx
x−
-
Created by T. Madas
Created by T. Madas
368. 1
xdx
x+
369. ( )2 2sec cosecx x x dx−
370. 24 4
2 1
x xdx
x
+
+
371. 2tanx x dx
372. 2cos 3x x dx
373. ( )23cos 6sin 2sin3x x x dx−
374. 2 4x x dx−
375. 3 2
3
6
xdx
x x
+
+
376. 1
1
xdx
x
−
−
377. 1
cosec2 cot 2dx
x x−
378. 3 5sec tanx x dx
379. ( )
3
cosh
cosh sinh
xdx
x x+
380. 2cos cos 3x x dx
-
Created by T. Madas
Created by T. Madas
381. 32
1
4
dx
x x+
382. ( )
2
2
cos 2sindx
x x+
383. ( )1ln 26 x dx+
384. 3
1 1
xdx
x+ −
385. ( )3
1
1dx
x x −
386. ( )125 31x x dx−
387. 1 12 4
1dx
x x−
388. 2
1
2 2 1dx
x x− +
389. 2
1
2dx
x x− −
390. 2
1
9 12 5dx
x x+ +
391. 2
1
16 8dx
x x−
392. 1
xdx
x−
-
Created by T. Madas
Created by T. Madas
393. 2
2
4
4 1
xdx
x +
394. cose sin cosx x x dx
395. ( )1229 4sin sinx x dx−
396. 2
2
1dx
x x+ −
397. 1
1 1dx
x x+ + −
398. cosh 2x dx
399. ( )2e tan secx x x dx+
400. 1
5
xdx
x
+
+
401. 2
1
1dx
x x −
402. ( ) ( )2 21 cos 1 cos sinx x x dx− + +
403. 2
3
1
xdx
x
+
+
404. 3 24 3 2 1
1
x x xdx
x
− + −
+
-
Created by T. Madas
Created by T. Madas
405. 2
1
1dx
x x+ +
406.
( )322
9
9
dx
x−
407. 3
2dx
x x−
408. 2
1
36dx
x +
409. 2
21
xdx
x−
410. 1
xdx
x +
411. 2
1
9 64dx
x +
412. 2 1
xdx
x +
413. 2
2 1
xdx
x +
414. ( )123 21x x dx−
415. sinh coshx x dx
416. 4 2 16
1 16
x x
xdx C
+ ×+
+
-
Created by T. Madas
Created by T. Madas
417. 3
sin
cos cos
xdx
x x+
418. sinh x dx
419. sech
cosh sinh
xdx
x x−
420. 1 sin
1 sin
xdx
x
+
−
421.
( )322
4
4
dx
x −
422. ( )14sinh 4 x dx
423. 1 cos
1 cos
xdx
x
−
+
424. 1
5 4cosdx
x+
425. 2cosh 2x dx
426. 2
1
3 2dx
x x+ −
427. 1
1 sin 2dx
x+
428. 2
588
4 49dx
x +
-
Created by T. Madas
Created by T. Madas
429. 2
1
9
xdx
x
+
+
430. e 1x dx−
431. e
e e
x
x xdx
−+
432. 21 e x dx−
433.
( )522
16
4
dx
x +
434. ( )3
21 x dx−
435. ( )cosh arctan sinhx x dx
436. sec x dx
437. 1
sec 1dx
x −
438. sin
1 tan
xdx
x−
439. 2
cos
cos 4sin 5
xdx
x x+ −
440. 2cos
cos sin
xdx
x x+
-
Created by T. Madas
Created by T. Madas
441. ( )2
18
cos 4sin 5 cosdx
x x x+ −
442. 2
tan
1 sin
xdx
x+
443. ( ) 11 exx dx++
444. 4tan secx x dx
445. ( )
4
1 sin cosdx
x x−
446. 2
2
1 4
xdx
x
+
−
447. 2
4 1
4 9
xdx
x
+
−
448. ( )8 ln 2 1x x dx+
449. cos3 sin 6x x dx
450. 4
3 5cosdx
x+
451. arctan x dx
452. 2
4cot
1 cos
xdx
x+
-
Created by T. Madas
Created by T. Madas
453.
( )2
2
18
9
dx
x +
454. e coshx x dx
455. ( )
32
2
1xdx
x x
+
−
456.
( )32
4
5 1
xdx
x −
457. 2
9
e e 9x xdx
−
458. 2
1
1dx
x x− −
459. 3
2
1 3
1
xdx
x
−
−
460.
( )3
2
8
1
dx
x+
461. 4
10 1
xdx
x −
462. 2
4
e e 4x xdx
+
463. 3
2
1dx
x+
-
Created by T. Madas
Created by T. Madas
464. arcoshx x dx
465. ( )3 2 25 2 e xx x dx+ −
466. 2
1
2dx
x x −
467. 1
1
xdx
x
+
−
468. 3 3sin 2 2sin3 cosx x x dx−
469. 2
25
25dx
x+
470. 3
4
2dx
x x+
471. 2
1
4dx
x −
472. 24coth 2x dx
473. 2
2 16
xdx
x −
474. 2
arctan
1
xdx
x+
475. 2
1
25 9dx
x−
-
Created by T. Madas
Created by T. Madas
476. 2
1
xdx
x
+
−
477. 2
e
e 9
x
xdx
−
478. 21x x dx−
479. 2
1 4
x
xdx
−
480. 3
2
cos sindx
x x
481. 1
1 sin cosdx
x x+ +
482. 3
2
4e
1 e
x
xdx
+
483. 2
e
9 e
x
xdx
−
484. 2
cos
1 sin
xdx
x+
485. ( )( )
1
e 1 e 1x xdx
+ −
486.
( )32
2
21
xdx
x−
487. 1
5cosh 4sinhdx
x x+
-
Created by T. Madas
Created by T. Madas
488. 2
3
4
xdx
x
+
−
489. 1 cos
1 sin
xdx
x
−
−
490. 3sin cos 3
cos sin
x xdx
x x
− +
+
491. 2
4 1
16
xdx
x
−
+
492. 2
1
4 4 2dx
x x+ +
493. 2
1
1 8sindx
x+
494. 3
1
sin cosdx
x x
495. 2
sin
16 9cos
xdx
x+
496. 4sinh cothx x dx
497. 5cos sin
3cos 2sin
x xdx
x x
−
+
498. 2
3 4
2 17
xdx
x x
−
+ +
499. 2
4
8 3
xdx
x x
+
+ +
500. ( )arsinh x dx
-
Created by T. Madas
Created by T. Madas
501. 2
1
2 7 3dx
x x+ +
502. 2
10sinh 2
cosh 2
xdx
x
503. arctanx x dx
504. ( )
2
sin ln xdx
x
505. ( )( )21 1
xdx
x x x+ + +
506. ( )2xx dx
507. 2 31 1e sinh e e6 2
x x xx dx C= − +
508.
( )32
2
2 8
xdx
x +
509. ( )2ln 1 x dx+
510. 2
cosh3
sinh 3
xdx
x
511. 4
5 3cosdx
x−
512. 2sinh x dx
-
Created by T. Madas
Created by T. Madas
513. 2sech 4x dx
514. 2
1
64 9dx
x+
515. 2
8
16 1dx
x −
516. 2
1
cosdx
x x
517. ( )
2
6
1 cosdx
x+
518. ( ) ( )2 2
3 2 2sin cos sin sin cosx x x x x dx+
519. ( )
2
2
3 2 5
3
x xdx
x
− +
+
520. 2
1
1dx
x x+ +
521. 225 x
dxx
−
522. 2
1
5 4dx
x x− −
523. e sinx x dx
-
Created by T. Madas
Created by T. Madas
524. 2
3 2
2 5 1
2
x xdx
x x x
+ −
+ −
525. 2
3 e sinxx x dx
526. tan x
dxx
527. ( )
2
2
2
xdx
x x
+
−
528. 1
1 exdx
+
529. 3cosec x dx
530. 2
1
e 3ex xdx
−
531. cosh
1 sinh
xdx
x+
532. 1
6sinh 2 9cosh 2dx
x x+
533. 2 21 4sinh coshx x dx+
534. 2
arsinh
1
xdx
x +
535. 2 1
xdx
x +
-
Created by T. Madas
Created by T. Madas
536. 2 4x dx+
537. 1 12 4
1
4 1
dx
x x
+
538. 2
6
6
1 4
xdx
x−
539. 2
21
xdx
x−
540. 2
1
4dx
x−
541. 22
1 21 dx
x x
− +
542. 2 4x dx−
543. 2
1
1dx
x x+ +
544. 2
1
9dx
x +
545. 1
1dx
x x+
546.
( )3
2
1
1
dx
x x+
-
Created by T. Madas
Created by T. Madas
547. 2
sin cos
cos 3cos 2
x xdx
x x+ +
548. ( )sin ln x dx
549. ( )1sinh 2 x dx−
550. ( ) ( )cos ln sinx x dx
551. 21 x dx−
552. 2
3
4 13dx
x x− +
553. 5
sin
cos
xdx
x
554. 23tanh x dx
555. 2
1
4 13dx
x x− +
556. 4
3
4dx
x−
557. 2
1
16 9dx
x −
558.
( )322
4
4
dx
x x−
-
Created by T. Madas
Created by T. Madas
559. cosh x dx
560. 2sinh sechx x dx
561. 2
1
2dx
x x−
562. 4
8
1dx
x −
563. ( )2
1
1dx
x x +
564.
( )2
1
1 ln
dx
x x−
565. ( )
2
6
1 cosdx
x+
566. 1
xdx
x+
567. 15
4cos 3sindx
x x+
568. ( )e 2cos 3sinx x x dx−
569. 2log x dx
570. 1 cos3x dx+
-
Created by T. Madas
Created by T. Madas
571. 3
81
xdx
x+
572. ( )ln x x dx+
573. sin sin 2x x x dx
574. cos
sin 2cos
xdx
x x+
575. 2
4
xdx
x
−
−
576. 3
2
sinh
cosh
xdx
x
577. 2
2
sec
4 tan
xdx
x+
578. 2
4 5
2 2
xdx
x x
+
+ +
579. ( ) ( )
1 12 2
1
2 4dx
x x− −
580. 3
2
xdx
x −
581. 3
5 exx dx
582. ( )( )
2
2
12 6
3 2
x xdx
x x
− −
− +
-
Created by T. Madas
Created by T. Madas
583. ( )3 1sin sin 2x x dx
584. cot
1 cos 2
xdx
x−
585. 5tan secx x dx
586. 4
2cosh sinh
1 cosh
x xdx
x+
587. 3
2
cos
sin
xdx
x
588. ( ) ( )1 15sin cos3 6x x dx
589. arcsin x dx
590. 2 2 2x x dx+ +
591. 2
cos
1 sin
xdx
x+
592. 2
3
2 2
1
x xdx
x
− −
−
593. ( )( )
3 2
2
3 4 5 2
1 1
x x xdx
x x
− + −
− +
594.
( )
2
22
8 29 10
2
x xdx
x x
− −
− −
-
Created by T. Madas
Created by T. Madas
595. 1
1
xdx
x
−
+
596. 2
4 tan
1 cos
xdx
x+
597. 2 2
1
1dx
x x −
598. ( )
1
1 2dx
x x+ +
599. ( )( )
1
6 2 2dx
x x x+ − +
600. ( )2
1
1dx
x x−
601.
( )2 21
1 1dx
x x+ −
602. ( ) 2
1
1 4 2dx
x x x+ + +
603. 236 x dx−
604.
( )322
2
4 1
xdx
x x
+
+ +
605. 1 4
xdx
x−
-
Created by T. Madas
Created by T. Madas
606. 2
1 sin 2cosdx
x x+ +
607. ( ) 2
1
2 1dx
x x x+ +
608. ( )ln 2 1
2 1
xdx
x
−
−
609. ( )cos ln x dx
610. arcsin x dx
611. 2
1
16dx
x −
612. ( )
4 3 2
5
3 2 2
1
x x x xdx
x x
+ + + −
+
613. arcsin
2
e
1
x
dx
x−
614. 3 2
4
xdx
x
+
615. 2
2 1
9
xdx
x
+
−
616. sinh
cosh 1
xdx
x −
617. 2
1
1dx
x x−
-
Created by T. Madas
Created by T. Madas
618. 2
1
2dx
x x−
619. ( ) ( )2 2
3
4 5 1 3 1dx
x x x+ − − −
620. 2 2
1
4dx
x x−
621. 2
arcsin
1
xdx
x−
622. 2
3
3 2 1dx
x x x+ −
623. 2
3
2dx
x x +
624. 2
1
1 sindx
x+
625.
2
2
sin
1 cos
xdx
x+
626. 4
2
1
xdx
x +
627.
( )
2
22
1
1
xdx
x
−
+
628.
2
2
2
2
e
1 2e
x
x
xdx
+
-
Created by T. Madas
Created by T. Madas
629. 5
3
1
1
x xdx
x
+ −
+
630. 4 4sin cosx x dx
631. 4
2
1dx
x x −
632. 4
2
1
xdx
x −
633. 6
8
sin
cos
xdx
x
634. 2cot 3 cosec3x x dx
635. 6sinh
sinh cosh
xdx
x x+
636. ( )2
2 4x x dx
−−
+
637. ( )( )2 2
12 1
6 1 6 5 10
xdx
x x x x
−
− − − + +
638. 1
xdx
x −
639. ( )( )
3 24 12 22 3
4 1
x x xdx
x x
− − −
− +
640. ( )2ln 1x x dx+
-
Created by T. Madas
Created by T. Madas
641.
( )
4 3
22
3 1
1
x x xdx
x x
+ + −
+
642. 3
6
1dx
x+
643. 2cos
cos sin
xdx
x x−
644. 3sec x dx
645. 4
1dx
x x+
646. 2
1
8 17dx
x x+ +
647. 2 3cosx x dx
648. 2
1
16 1dx
x +
649. 1
2 cosdx
x+
650. ( )sin
1sin4
xdx
x π+
651. 1
tanh tandx
x x+
652. ( )
( )
2
4
2 1
1
xdx
x x
+
+
-
Created by T. Madas
Created by T. Madas
653.
( )342 4
1
1
dx
x x+
654.
( )21
1
dx
x x x− −
655. 2 1x
dxx
−
656. ( )2 2
3
2 tan sec
1 tan
x x
dxx
+
+
657. 3
1 1
1 1
xdx
x x
+ +
+ + +
658. sech x dx
659. 2
2 3
9
xdx
x
−
−
660. 1
1 tandx
x+
661. 31
xdx
x−
662. 2 1x dx−
663. ( ) ( )
2 2
4sin3
cos7 cos sin 7 sin
xdx
x x x x+ + +
-
Created by T. Madas
Created by T. Madas
664. 4
4
4
xdx
x+
665.
( )
2
22
12
1
xdx
x −
666. 2
2
2 cot
cosec
x x xdx
x x
+
+
667. 1 tan
1 tan
xdx
x
−
+
668. tan
sin 2
xdx
x
669.
( )2
2
16
4
dx
x +
670. arcsec x dx
671. 2
1 2
xdx
x−
672. ( )
2
1
1
xdx
x x
−
+
673. 22e e 1x x dx−
674. 3
1dx
x x+
675. 1
1 sin 2dx
x−
-
Created by T. Madas
Created by T. Madas
676. ( )2 2e 3sec 2sec tan 2 tanx x x x x dx+ +
677. 3 tan x dx
678. ( )2 3
2 3
e xx x
dxx
−
+
679. ( )
( )2
6
2
xdx
x
+
+
680.
( )322
9
4 24 27
dx
x x− +
681. 2
4
x xdx
x
−
682.
( )2
2
16
2 5
dx
x x− +
683. 2 2
tanh
sech tanh
xdx
x x−
684. 2
1
4dx
x x x+ +
685.
( )3225 4
xdx
x x− −
686. ( )5221 x dx−
-
Created by T. Madas
Created by T. Madas
687. 4 2 1
xdx
x x+ +
688.
( )3
2
8
1
dx
x +
689. 2
1 cos
sin
xdx
x
+
690. 4
2 4
1
1
xdx
x x
−
+
691.
( )3
2
9
2 2
xdx
x x
+
+ +
692. 2
3 3
sec 1
sec tan
xdx
x x
−
+
693. tan sec 2x x dx
694. ( )( )
5cos
2 sin 3 4sin
xdx
x x+ +
695. ( )
( )2
3
3 3e sin
1
xx xx dx
x
−+ +
+
696. 6 6
2 2
sin cos
sin cos
x xdx
x x
+
697.
( )
2 2
23 3
3sin cos
cos sin
x xdx
x x−
-
Created by T. Madas
Created by T. Madas
698. 8 8
2
sin cos
11 sin 22
x xdx
x
−
−
699. 212 arctanx x dx
700. tan x dx
701. 3
2 4
cot
1 2cot 2cot
xdx
x x+ +
702. ( )2
22 1 exx dx+
703. 11
1 ex
xx dxx
+ + −
704. 6 6
1
cos sindx
x x+
705. e 1x dx−
706. 1
e 1xdx
−
707. 4 2
1
3 2dx
x x+ +
708. 2
2
1arccos
1
xx dx
x
−
+
709. 2 22 sec tanx x x dx
-
Created by T. Madas
Created by T. Madas
710. ( )ln 1x x dx+ +
711. 3sin 4cos
2sin cos
x xdx
x x
+
−
712. 4
4
1dx
x x +
713. ( )
( )
2
2
3 5
1
x x x
dx
x
+
+
714.
( )322
4
4
dx
x −
715. ( )
1
1 1 2dx
x x− −
716. tan cotx x dx−
717. ( )( )1 5x x dx+ −
718. 33
8 8dx
x x
+
719. ( )
2
1
1
xdx
x x
−
+
720. 24sin sin 2 sin 3x x x dx
721. 2sec
sec tan
xdx
x x+
-
Created by T. Madas
Created by T. Madas
722. ( )( )
2
1ln ln
lnx dx
x
+
723. ( )( )2 5 2 3x x dx+ −
724. 2
3
1
xdx
x x− −
725. ( )
( )
2
2
1 e
1
xx
dx
x
+
+
726. ( )
( )2
3
1
x xdx
x
+
+
727. ( )
2
2
2
2cos sin
xdx
x x x
+
+
728. ( )2 2
4
ln 1 2ln 1x x xdx
x
+ − +
729. arcsin arccos
arcsin arccos
x xdx
x x
−
+
730. ( )
( )
3
4
e 6 5
2 1
xx
dx
x
−
−
731. ( )
23
4
1 2
1
xdx
x x
−
+
732. 4
1
1dx
x +
-
Created by T. Madas
Created by T. Madas
733. ( )
2
2cos sin
xdx
x x x−
734. 6
1
1dx
x +
735. 2
4 2
1
1
xdx
x x
+
− +
736. 2
2
arctan
1
x xdx
x+
737. 41
xdx
x+
738. 1
1 cotdx
x−
739. ( )2
5
sin xdx
x
−
740. ln3 x dx
741. 5tan x dx
742. 3 3tan secx x dx
743. 3sec cosecx x dx
744. cos
cos 2
xdx
x
745. 6sec x dx
-
Created by T. Madas
Created by T. Madas
746. 3
ln xdx
x
747. 44 1x x dx+
748. ( )2
1
1 3sin lndx
x x +
749. 2ln 2 4 1x x dx + −
750. ( )2ln 1x dx−
751. e e 1
e 2
x x
xdx
−
−
752. 2 2
1
1dx
x x +
753. 2
2
4xdx
x
+
754. 1 cos
1 cos
xdx
x
+
−
755. ( )tan ln secx x dx
756. 2
arctan xdx
x
757. 2
sin cos ln
cos
x x x xdx
x x
+
-
Created by T. Madas
Created by T. Madas
758. ( )2 4
4 4
1
2
x x
dx
x
+
+ 759. 1 tan x dx+
760. 2 1x x dx+ +
761. ( )cos 4arcsin x dx
762. ( )cos artanh cosx x dx
763. 2 2
cos sin
cos sin
x xdx
x x+
764. 7
1dx
x x−
765. 8 3
1dx
x x−
766. 1
1
xdx
x
−
−
767. 4
4
sech tanh
1 sech
x xdx
x−
768. 2
1 arcsin
1 arcsin
xdx
x x
−
−
769. 2
4 3 2
2e e
e 2e e 1
x x
x x xdx
+
+ + +
-
Created by T. Madas
Created by T. Madas
770. ( ) 2
1
2 1dx
x x+ −
771. 4 1
2 1
x
xdx
+
+
772. ( )sin 2 sin sinx x dx
773.
( )
2
2 4
1
1 1
xdx
x x
+
− +
-
Created by T. Madas
Created by T. Madas
![COMPUTER BASED TEST (CBT) Memory Based Questions & … · x2= 4b(y + b), tgk¡ b ,d izkpy gS] dk vody lehdj.k gksxk % (1) 2 2 x dx dy 2 dx dy x (2) x dx dy 2y dx dy x 2 (3) 2 2 x](https://img.pdfslide.us/doc/110x75/5f0a7c707e708231d42bdeef/computer-based-test-cbt-memory-based-questions-x2-4by-b-tgk-b-d.jpg)
![Differential Geometry Jay Havaldar v[x] = dx dx v1 + dx dy v2 + dx dz v3 = v1 Intermsofthegradient: dx= v[x] = (1;0;0) v= v1 In other words, the differentialdxis a function which sends](https://img.pdfslide.us/doc/110x75/5b1ce2f07f8b9af2348c42c4/differential-geometry-jay-havaldar-vx-dx-dx-v1-dx-dy-v2-dx-dz-v3-v1-intermsofthegradient.jpg)
