Created by T. Madas Created by T. Madas INTEGRATION MIX (WITHOUT ANSWERS)
Created by T. Madas
Created by T. Madas
INTEGRATION
MIX (WITHOUT ANSWERS)
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 4
dx
x−∫
13. ( )1 2cos sinx x dx+∫
14. 2 12cos cos2
x 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 xdx
−+∫
19. ( )
3
6
3 2dx
x +∫
20. ( )
3
6
3 2
xdx
x +∫
21. ( )sin 2cos sinx x x dx−∫
Created by T. Madas
Created by T. Madas
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∫
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
4 2
xdx
x +∫
35. ( )( )
2
2 4dx
x x− −∫
36. 3
4 1dx
x +∫
37. 2
11 dx
x
+
∫
38.
( )3
2 1
xdx
x −∫
39. 1
xdx
x +∫
40. cos sinx x dx−∫
41. sin cosx x dx−∫
42. ( )sin 4 3x dx+∫
Created by T. Madas
Created by T. Madas
43. ( )cos 5 2x dx−∫
44. 3sin 2x dx∫
45. ( )2sin 1 secx x dx+∫
46. ( )2
1 2cos x dx−∫
47. ( )2 2sec 1 cotx x dx+∫
48. 2 cos3x x dx∫
49. ( )( )
3
2 1dx
x x+ −∫
50. ( )4
3 1x dx+∫
51. ( )123 2 1x dx+∫
52. 2 2
1
cos tandx
x x∫
53. cos sinx x dx∫
54. 2
2
cosdx
x∫
55. 22 2 tan 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
1 2dx
x x+ +∫
61. ( )1
4 5x dx−
−∫
62. 1
4dx
x∫
63. 1x
dxx
+
∫
64. 1
xdx
x +∫
65. 2
4
1 2
xdx
x−∫
Created by T. Madas
Created by T. Madas
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 2sec 1 tanx x dx+∫
72. ( )2sec 1 tanx x dx+∫
73. ( )2cosec 3 1x dx+∫
74. ( )212sec 2 3x dx+∫
75. sin x
dxx∫
76. 2 26e xdx
+∫
77. ( )2 2sec 1 cotx x dx−∫
78. sin cos
sin cos
x xdx
x x
−
+∫
79. sec tan sec 1x x x dx+∫
80. tan 2 sec 2x x dx∫
81. 2 lnx x dx∫
82. 2
6
2 8dx
x x− −∫
83. 23cot x dx∫
84. cos2 sinx x dx∫
85. 2 4x
dxx
+∫
86. 2
34
xdx
x−∫
87. ( )527 2 3x dx−∫
88. ( )1sin2
x x dx∫
Created by T. Madas
Created by T. Madas
89. 1
xdx
x −∫
90. 2
4
4 4 1dx
x x+ +∫
91. 3
4 1dx
x +∫
92. 4 1
2 5
xdx
x
+
−∫
93. ( )
12
1
3 2dx
x −∫
94. 6 3
2
xdx
x
+
∫
95. 2
4
1
xdx
x −∫
96. 2
2 1
xdx
x −∫
97. ( )( )
2
17 5
2 3 2
xdx
x x
−
+ −∫
98. 4
2
1 cos
cos
xdx
x
+
∫
99. ( )sin 2 1x x dx−∫
100. ( )3
4 3 2x dx−∫
101. x x dx∫
102. 32 2
1dx
x x∫
103. 3
2 4dx
x−∫
104. 1
1 cos 2dx
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. 6
2 3
xdx
x +∫
110. ( )( )
14 1
1 2 1
xdx
x x
+
− +∫
Created by T. Madas
Created by T. Madas
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. 2secx x dx∫
116. 2
2
3e
e 1
x
xdx
−∫
117. cosec2 cot 2x x dx∫
118. 2 2tan secx x dx∫
119. ( )2
2cos 3sinx x dx−∫
120. sin 2 cosecx x dx∫
121. sin tan
cos
x xdx
x
+
∫
122. 2
1 sin
cos
xdx
x
+
∫
123. sine cosxx 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
− +
− −∫
128. 3 1
2 3
xdx
x
−
+∫
129. 28
1 2
xdx
x−∫
130. ( )
32
10
3 1
dx
x +∫
131. 5xdx∫
132. 2sin cosx x dx∫
Created by T. Madas
Created by T. Madas
133. ( ) ( )22 1 sin 1x x x dx+ + +∫
134. ( ) ( )21 cos 2 1x x x dx+ + +∫
135. ( )( )22 1 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∫
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. 2
1 2 tan
cos
xdx
x
+
∫
149. 2sec tan 1 tanx x x dx+∫
150. 2tan x dx∫
151. ( )
2
2
1 sin
cos
xdx
x
+
∫
152. 2cos
1 sin
xdx
x+∫
153. 1
1 cosdx
x+∫
154. cos
sin
xdx
x∫
Created by T. Madas
Created by T. Madas
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
+
∫
166. 1
lndx
x x∫
167. ( )2
2 3x dx−
−∫
168. 2 12sec sin 2
2x x dx+∫
169. 4cos
sin
xdx
x∫
170. ln x
dxx∫
171. 2 26 tan secx x dx−∫
172. 4 24cos 2sinx x dx−∫
173. sin 4 cos 4x x dx∫
174. 1
cosec cotdx
x x−∫
175. 2
1
xdx
x +∫
Created by T. Madas
Created by T. Madas
176. 23e
e 1
x
xdx
−∫
177. ( )
1
2dx
x x+∫
178. 7
4
4
1
xdx
x +∫
179. 3
1
xdx
x+∫
180. 29 1
xdx
x +∫
181. 3
2dx
x x+∫
182. 23 2
4 1
xdx
x
+
+∫
183. 2 3
3 4 2dx
x x x+ −∫
184. ( )( )
2
2
10 23 11
2 3 2 1
x xdx
x x
− +
− −∫
185. 22sin 2 cosx x dx∫
186. sin sin3x x dx∫
187. sec
sec tan
xdx
x x−∫
188. cos5x x dx∫
189. 1
4cos3 sin32
x x dx+∫
190. 2 1 1sin 2 sin 4
2 8x dx x x C= − +∫
191. 2cos3 sinx x dx∫
192. 2
cos 2
1 cos 2
xdx
x−∫
193. 33cos 3x dx∫
194. 43sec x dx∫
195. 2sin
cos sin
xdx
x x+∫
196. 2 4
1
cos tandx
x x∫
197. 4 1
2 1 3 4dx
x x+
− −∫
198. 2 sin3x x dx∫
Created by T. Madas
Created by T. Madas
199. 2cosec 2x d∫
200. 3sin 2 cos 2x x dx∫
201. 2cot 3x dx∫
202. 7
3dx
x∫
203. sin cos
1 cos 2
x xdx
x−∫
204. sin cos
cos 2 1
x xdx
x +∫
205. ( )5
4 3 2x dx−∫
206. 1 sin
cos
xdx
x
+
∫
207. sin 2 sinx x dx∫
208. 2cosx x dx∫
209. sin 2 secx x dx∫
210. ( )13sin 1x dx+∫
211. 2
1 ln xdx
x
−
∫
212. 234 e
xx dx
−
∫
213. ( )2
exx 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∫
218.
2
2
2
2
4 e
1 2e
x
x
xdx
+∫
219. 2
1
cos tandx
x x∫
220. sin 2
1 cos
xdx
x+∫
221. ( )
4
3 2 1dx
x +∫
Created by T. Madas
Created by T. Madas
222. 3sin x dx∫
223. 2
1
sin cosdx
x x∫
224. 1 1
sin 2 cos33 2
x x dx−∫
225. 2
3
4 2
xdx
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 1cos3
x x dx∫
231. ( )( )
3
2 1dx
x x− +∫
232. ( )( )
1
2 2dx
x x− +∫
233. 4 3
2 1
xdx
x
−
+∫
234. 1
1x dxx
+
∫
235. 2
2
2
1
xdx
x
−
−∫
236. ( )2
1
1dx
x x −∫
237. sec
cos sin
xdx
x x−∫
238. 1
1 1dx
x+ −∫
239. 32
26
2 1
xdx
x −∫
240. 1
5
xdx
x
+
−∫
241. ( )
22
3
xdx
x
+
∫
242. 2 14e sin 3
3
xx dx
−−∫
Created by T. Madas
Created by T. Madas
243. 22 sec 2x x dx∫
244. 3cos sinx x dx∫
245. 5
7
sin
cos
xdx
x∫
246. tan 3x dx∫
247. 1
sec 1dx
x −∫
248. 2
4
sin
cos
xdx
x∫
249. sin cos
1 cos
x xdx
x−∫
250. 2e 2e
e 1
x x
xdx
−
+∫
251. ( )
14 1
4
xdx
−−
∫
252. 22 3 2
1
x xdx
x
− +
−∫
253. 2
4 2
1xdx
x x
+
−∫
254. 4cosec x dx∫
255. 21 cot x dx−∫
256. 122 e
xx dx∫
257. ( )2
e 2ex xdx
−+∫
258. ( )e sin ex xdx∫
259. 2ex dx∫
260. ( )2
2cos 3x dx−∫
261. 2
2
xdx
x −∫
262. 4 1x
dxx
+
∫
263. ( )
3
11 e xx
dx
x
+
∫
264.
( )322
1
1
dx
x−∫
265. 2
2 1
x
xdx
+∫
Created by T. Madas
Created by T. Madas
266. ( )2 1 2 3x x dx− −∫
267. 5
3
9
1
xdx
x +∫
268. ( )2
3sin cos x dx−∫
269. 2
4
10
xdx
x −∫
270. 3
3
4e
1 e
x
xdx
−∫
271. ( )sin cos 1 cosx x x dx−∫
272. ( )2
tan 1x dx−∫
273. 1 e
1 e
x
xdx
+
−∫
274. 1
e 1xdx
+∫
275. 1
sin cosdx
x x∫
276. 2
1
cos sindx
x x∫
277. sin3 cos 2x x dx∫
278. 4sin 2 cos 2x x dx∫
279. 1
1 sindx
x−∫
280. ( )sin 2 1 sinx x dx+∫
281. sec tanx x x dx∫
282. ( )
2
1 2
4 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
+
+ +∫
Created by T. Madas
Created by T. Madas
288. sin 2 cosx x dx∫
289. sin 2 cos 2x x dx∫
290. 3
3 1
x
xdx
+∫
291. ( )
2ln x
dxx∫
292. 31
x dxx∫
293. tan
sec tan
xdx
x x−∫
294. ( )
( )( )
2
2
8 1
3 1
x
dx
x x
+
− +∫
295. ( )( )4
21 2 1x x x dx+ + +∫
296. 4sin cosx x dx∫
297. 3
2
3 5
1
x xdx
x
+
+∫
298. 2
2 6
6 1
xdx
x x
+
+ +∫
299. ( )
1
2dx
x x −∫
300. 2sin 2x dx∫
301. 2
cos2
cos
xdx
x∫
302. tan
1 cos2
xdx
x+∫
303. 3sec tanx x dx∫
304. 2 2cos sinx x dx∫
305. ( )2
ln 1x x dx − ∫
306. 2
3 1
xdx
x +∫
307. 2 1
3 1
xdx
x
+
−∫
308. ( )4
23x x dx+∫
309. 2 2
9
9dx
x x−∫
310. 3
1 2
xdx
x
−
+ −∫
Created by T. Madas
Created by T. Madas
311. 2
1
4dx
x −∫
312. 3
cos
sin
xdx
x∫
313. 2sin
cos sin
xdx
x x+∫
314. ( )2
21 x dx−
−∫
315. cos sinx x dx∫
316. ( )2
sin 2cosx x dx+∫
317. 2 2
1
sin cosdx
x x∫
318. sin sin cos
1 cos
x x xdx
x
+
−∫
319. 4
1
cosdx
x∫
320. ( )
2
3
sec
1 tan
xdx
x+∫
321. sin cos
cos 2 1
x xdx
x +∫
322. cot 2x dx∫
323. 2ln x
dxx∫
324. ( )2 1sin cos2
x x dx∫
325. 3e 1
e 1
x
xdx
+
+∫
326. 2xdx∫
327. 2 3x xdx∫
328. 2 13 xdx
+∫
329. 1
xdx
x −∫
330.
32
52
2 1
2
xdx
x x
+
+∫
331. ( )
1
1dx
x x+∫
332. ( )2
1
1dx
x x+∫
333. 1
xdx
x −∫
Created by T. Madas
Created by T. Madas
334. 2
2
2 2
2 2
x xdx
x x
+ −
− +∫
335. ( )2
tan cotx x dx+∫
336. 3sin sin 2x x dx∫
337. sin cosx x x dx∫
338.
14
54
2 1
4 4
xdx
x x
+
+∫
339. 1
cosec cotdx
x x−∫
340. 3sec tanx x dx∫
341. eex
xdx
+∫
342. ( )ln 1x
dxx
−
∫
343.
( )2
1
1
dx
x x+∫
344. e x
dxx∫
345. e xx dx∫
346. 2 e xx dx
−∫
347. e cosxx dx∫
348. 2
2
5
5 3
x
xdx
+∫
349. ( )( )
24 1
1 2 1
x xdx
x x
− +
− −∫
350. 5
3
3
1
xdx
x −∫
351. ( ) 2
1
1 1dx
x x− −∫
352. 2
2
4 2
xdx
x x
−
− −∫
353. 3 2
2
3 10 3
3
x x xdx
x
− + −
+∫
354. 2
cos tan
1 tan
x xdx
x
+
+∫
355.
( )322
4
4
dx
x+∫
Created by T. Madas
Created by T. Madas
356. ( )
2
2
1
1
xdx
x
+
+∫
357. 3 4
4
4 1
1 1
x xdx
x
+
+ +∫
358. ( )2
ln x dx∫
359. 1x
dxx
+∫
360. 2 5
1dx
x x+∫
361. ( )22sin cos 1x x dx+ −∫
362. ( )sin cosx x x dx+∫
363. 1
2 3
1 1e x dx
x x
+
∫
364. 18cos sin 2x x dx∫
365. ( )
3
cos
cos sin
xdx
x x+∫
366. 4sec
tan
xdx
x∫
367. 1
xdx
x−∫
368. ( )2 2sec cosecx x x dx−∫
369. 24 4
2 1
x xdx
x
+
+∫
370. 22 tanx x dx−∫
371. 24 cos 2x x dx∫
372. ( )23cos 6sin 2sin 3x x x dx−∫
373. 2
20
4
xdx
x−∫
374. 1
1
xdx
x
−
−∫
375. 3 2
3
6
xdx
x x
+
+∫
376. 2 4x x dx−∫
377. 1
cosec2 cot 2dx
x x−∫
Created by T. Madas
Created by T. Madas
378. 3 5sec tanx x dx∫
379. ( )
3
cosh
cosh sinh
xdx
x x+∫
380. 2cos cos 3x x dx∫
381. 12
1
4
dx
x x+∫
382. ( )1ln 26
x dx+∫
383. 3
1 1
xdx
x+ −∫
384. ( )3
1
1dx
x x −∫
385. 5 31x x dx−∫
386. 1 12 4
1dx
x x−∫
387. 2
1
2 2 1dx
x x− +∫
388. 2
1
2dx
x x− −∫
389. 2
1
9 12 5dx
x x+ +∫
390. 2
1
16 8dx
x x−∫
391. 1
xdx
x−∫
392. 2
2
4
4 1
xdx
x +∫
393. cose sin cos
xx x dx∫
394. ( )122sin 9 4cosx x dx−∫
395. ( )
2
4
cos 2sindx
x x+∫
396. ( ) ( )22
1 cos sin cos 1x x x dx− + +∫
397. 2
2
1dx
x x+ −∫
398. 1
1 1dx
x x+ + −∫
Created by T. Madas
Created by T. Madas
399. cosh 2x dx∫
400. ( )2e tan sec
xx x dx+∫
401. 2
1
1dx
x x −∫
402. 1
5
xdx
x
+
+∫
403. 2
3
1
xdx
x
+
+∫
404. 3 24 3 2 1
1
x x xdx
x
− + −
+∫
405. 2
1
1dx
x x+ +∫
406.
( )322
9
9
dx
x−∫
407. 2
21
xdx
x−∫
408. ( )2
2
1dx
x x −∫
409. 2
1
1dx
x +∫
410. 2
1
9 64dx
x +∫
411. 2 1
xdx
x +∫
412. 2
2 1
xdx
x +∫
413. 1
xdx
x +∫
414. 3 21x x dx−∫
415. 4 2 16
1 16
x x
xdx
+ ×
+∫
416. 3
sin
cos cos
xdx
x x+∫
417. sinh x dx∫
418. sech
cosh sinh
xdx
x x−∫
419. 1 cos
1 cos
xdx
x
−
+∫
420. 1 sin
1 sin
xdx
x
+
−∫
Created by T. Madas
Created by T. Madas
421. 2cosh 2x dx∫
422. 4sinh3x dx∫
423. sinh coshx x dx∫
424. 1
5 4cosdx
x+∫
425.
( )322
4
4
dx
x −∫
426. 1
1 sin 2dx
x+∫
427. 2
1
3 2dx
x x+ −∫
428. 2
588
4 49dx
x +∫
429. 2
1
9
xdx
x
+
+∫
430. e 1x
dx−∫
431. 21 e
xdx−∫
432. e
e e
x
x xdx
−+∫
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. ( )2
18
cos 4sin 5 cosdx
x x x+ −∫
441. 2cos
cos sin
xdx
x x+∫
Created by T. Madas
Created by T. Madas
442. 2
tan
1 sin
xdx
x+∫
443. ( ) 11 e
xx dx
++∫
444. 4tan secx x dx∫
445. ( )
4
cos 1 sindx
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. 4
5 3cosdx
x−∫
452. 2sinh x dx∫
453. 2sech 4x dx∫
454. 2
1
64 9dx
x+∫
455. 2
8
16 1dx
x −∫
456. 2
1
cosdx
x x∫
457. ( )
2
6
1 cosdx
x+∫
458. ( ) ( )2 2
3 2 2sin cos sin sin cosx x x x x dx+∫
459. ( )
2
3
3 2 5
3
x xdx
x
− +
+∫
460. 2
25 xdx
x
−∫
461. 2
1
1dx
x x+ +∫
462. e sinx
x dx∫
Created by T. Madas
Created by T. Madas
463. 2
3 2
2 5 1
2
x xdx
x x x
+ −
+ −∫
464. 2
1
5 4dx
x x− −∫
465. ( )
2
2
2
xdx
x x
+
−∫
466. 2
3e
xx dx∫
467. 1
1 exdx
+∫
468. 2
1
e 3ex xdx
−∫
469. 3cosec x dx∫
470. tan x
dxx∫
471. cosh
1 sinh
xdx
x+∫
472. 1
6sinh 2 9cosh 2dx
x x+∫
473. 2 21 4sinh coshx x dx+∫
474. 2
arsinh
1
xdx
x +∫
475. 2 1
xdx
x +∫
476. 24x dx+∫
477. 1 12 4
1
4 1
dx
x x
+
∫
478. 2
6
6
1 4
xdx
x−∫
479. 2
21
xdx
x−∫
480. 2
1
4dx
x−∫
481. 22
1 21 dx
x x
− +
∫
482. 2
1
9dx
x +∫
Created by T. Madas
Created by T. Madas
483. 2 4x dx−∫
484. 2
1
1dx
x x+ +∫
485.
( )3
2
1
1
dx
x x +∫
486. 2
sin cos
cos 3cos 2
x xdx
x x+ +∫
487. ( )sin ln x dx∫
488. ( )cos ln sinx x dx∫
489. 1
1dx
x x +∫
490. ( )1sinh2
x dx−∫
491. 23tanh x dx∫
492. 5
sin
cos
xdx
x∫
493. 21 x dx−∫
494. 2
3
4 13dx
x x− +∫
495. 2
1
4 13dx
x x− +∫
496. 44
xdx
x−∫
497. 2
1
16 9dx
x −∫
498. 2
1
2dx
x x−∫
499. 2sinh sechx x dx∫
500.
( )322
4
4
dx
x x−∫
501. cosh x dx∫
502. 4
8
1dx
x −∫
503. ( )2
1
1dx
x x +∫
504.
( )2
1
1 ln
dx
x x−∫
Created by T. Madas
Created by T. Madas
505. ( )
2
6
1 cosdx
x+∫
506. 5
4cos 3sindx
x x+∫
507. 1
xdx
x+∫
508. 2log x dx∫
509. ( )e 2cos 3sinxx x dx−∫
510. 1 cos3x dx+∫
511. 2
4
xdx
x
−
−∫
512. ( )ln x x dx+∫
513. sin sin 2x x x dx∫
514. cos
sin 2cos
xdx
x x+∫
515. 3
2
sinh
cosh
xdx
x∫
516. 2
2
sec
4 tan
xdx
x+∫
517. ( ) ( )
1 12 2
1
2 4
dx
x x− −∫
518. 2
4 5
2 2
xdx
x x
+
+ +∫
519. 3
2
xdx
x −∫
520. ( )( )
2
2
12 6
3 2
x xdx
x x
− −
− +∫
521. 3
5 exx dx∫
522. 3
81
xdx
x+∫
523. ( )3sin sin2x
x dx∫
524. cot
1 cos 2
xdx
x−∫
525. 5tan secx x dx∫
526. 4
2cosh sinh
1 cosh
x xdx
x+∫
Created by T. Madas
Created by T. Madas
527. 3
2
cos
sin
xdx
x∫
528. arcsin x dx∫
529.
( )
2
22
8 29 10
2
x xdx
x x
− −
− −∫
530. 2
3
2 2
1
x xdx
x
− −
−∫
531. 2 2 2x x dx+ +∫
532. ( )( )
3 2
2
3 4 5 2
1 1
x x xdx
x x
− + −
− +∫
533. 2
cos
1 sin
xdx
x+∫
534. 1
1
xdx
x
−
+∫
535. ( ) ( )5sin cos3 6x x
dx∫
536. 2
4cot
1 cos
xdx
x+∫
537. ( )
1
1 2dx
x x+ +∫
538. 2 2
1
1dx
x x −∫
539. ( )2
1
1dx
x x−∫
540. ( )( )
16
6 2 2dx
x x x+ − +∫
541.
( )2 2
16
1 1dx
x x+ −∫
542. ( ) 2
1
1 4 2dx
x x x+ + +∫
543.
( )322
2
4 1
xdx
x x
+
+ +∫
544. 236 x dx−∫
545. 1 4
xdx
x−∫
546. ( ) 2
1
2 1dx
x x x+ +∫
Created by T. Madas
Created by T. Madas
547. ( )cos ln x dx∫
548. ( )ln 2 1
2 1
xdx
x
−
−∫
549. ( )
32
2
1xdx
x x
+
−∫
550. 2
9
e e 9x xdx
−∫
551.
( )3
2
8
1
dx
x+∫
552. 3
2
1 3
1
xdx
x
−
−∫
553. 2
4
e e 4x xdx
+∫
554. arcsin x dx∫
555. arctan x dx∫
556. arcoshx x dx∫
557. e coshxx dx∫
558. 2
1
16dx
x −∫
559. 2
1
1dx
x x− −∫
560.
( )2
2
18
9
dx
x +∫
561. 3
2
1dx
x+∫
562.
( )32
4
5 1
xdx
x −∫
563. 4
10 1
xdx
x −∫
564. 2
1
4dx
x −∫
565. 24coth 2x dx∫
566. 3 3sin 2 2sin 3 cosx x x dx−∫
567. 2
arctan
1
xdx
x+∫
Created by T. Madas
Created by T. Madas
568. arcsin
2
e
1
x
dx
x−∫
569. 1
1
xdx
x
+
−∫
570. ( )3 2 25 2 e xx x dx+ −∫
571. 3
4
2dx
x x+∫
572. ( )
4 3 2
5
3 2 2
1
x x x xdx
x x
+ + + −
+∫
573. 2
25
25dx
x+∫
574. 2
1
25 9dx
x−∫
575. 2
1
2dx
x x −∫
576. 2
2 16
xdx
x −∫
577. 2
2 1
9
xdx
x
+
−∫
578. 2
1
1dx
x x−∫
579. 2 2
1
4dx
x x−∫
580. 2
1
3 2 1dx
x x x+ −∫
581. ( ) ( )2 2
3
4 5 1 3 1dx
x x x+ − − −∫
582. 2
1
2dx
x x−∫
583. 21x x dx−∫
584. 2 3
4
xdx
x
+∫
585. sinh
cosh 1
xdx
x −∫
586. 2
arcsin
1
xdx
x−∫
587. 2
1 4
x
xdx
−∫
Created by T. Madas
Created by T. Madas
588. 2
1
2dx
x x +∫
589. 3
2
4e
1 e
x
xdx
+∫
590. 2
e
9 e
x
xdx
−∫
591. 2
e
e 9
x
xdx
−∫
592. 2
1
xdx
x
+
−∫
593. 2
3
4
xdx
x
+
−∫
594.
( )32
2
21
xdx
x−∫
595. 1
1 sin cosdx
x x+ +∫
596. 3
2
sin cosdx
x x∫
597. 1
5cosh 4sinhdx
x x+∫
598. 2
cos
1 sin
xdx
x+∫
599. 1 cos
1 sin
xdx
x
−
+∫
600. 2
4 1
16
xdx
x
−
+∫
601. 2
1
4 4 2dx
x x+ +∫
602. 2
4 7
2 7 3
xdx
x x
+
+ +∫
603. 2
1
2 7 3dx
x x+ +∫
604. 10 tanh 2 sech 2x x dx∫
605. 3sinh coshx x dx∫
606. 3
1
sin cosdx
x x∫
607. 2
sin
16 9cos
xdx
x+∫
608. 2
1
1 8sindx
x+∫
Created by T. Madas
Created by T. Madas
609. 5cos sin
3cos 2sin
x xdx
x x
−
+∫
610. 3 3sin cos
sin cos
x xdx
x x
+ −
+∫
611. arctanx x dx∫
612. ( )arsinh x dx∫
613. ( )( )21 1
xdx
x x x+ + +∫
614. 2
3 4
2 4
xdx
x x
−
+ +∫
615.
( )32
2
2 8
xdx
x +∫
616. 1
xdx
x −∫ .
617. ( )( )
3 24 12 22 3
4 2 1
x x xdx
x x
− − −
− +∫
618. ( )2ln 1 x dx+∫
619.
( )
4 3
22
3 1
1
x x xdx
x x
+ + −
+∫
620. ( )
2
sin ln xdx
x∫
621. ( )2xx dx∫
622. ( )2ln 1x x dx+∫
623. 2e sinhxx dx∫
624. 3
6
1dx
x+∫
625. 3sec x dx∫
626. 6cosech3 coth3x x dx∫
627. 2cos
cos sin
xdx
x x−∫
628. 1
2 cosdx
x+∫
629. 2 3cosx x dx∫
630. ( )
( )
2
4
2 1
1
xdx
x x
+
+∫
Created by T. Madas
Created by T. Madas
631. 1
tanh tandx
x x+∫
632. ( )sin
sin4
xdx
x π+∫
633.
( )2
1
1
dx
x x x− −∫
634. ( )2 2
3
2 tan sec
1 tan
x x
dx
x
+
+∫
635. 2
2 3
9
xdx
x
−
−∫
636. 2 1x
dxx
−∫
637. 2
1
8 17dx
x x+ +∫
638. 3
1 1
1 1
xdx
x x
+ +
+ + +∫
639. 2 1xdx−∫
640. ( ) ( )
2 2
4sin 3
cos7 cos sin 7 sin
xdx
x x x x+ + +∫
641. sech x dx∫
642. arcsec x dx∫
643. 4
4
4
xdx
x+∫
644.
( )
2
22
12
1
xdx
x −∫
645. 2
1
16 1dx
x +∫
646. ( )
2
1
1
xdx
x x
−
+∫
647. 2
1 2
xdx
x−∫
648.
( )2
2
16
4
dx
x +∫
649. ( )
( )2
6
2
x xdx
x
+
+∫
650.
( )322
9
4 24 27
dx
x x− +∫
Created by T. Madas
Created by T. Madas
651. 22e e 1x xdx−∫
652. 2
4
x xdx
x
−∫
653. 1
1 sin 2dx
x−∫
654. 3
1dx
x x+∫
655. 2
1
2dx
x x x+ +∫
656. 2
2
2 cot
cosec
x x xdx
x x
+
+∫
657.
( )3225 4
xdx
x x− −∫
658. ( )2 2e 3sec 2sec tan 2 tanxx x x x dx+ +∫
659. ( )5221 x dx−∫
660. ( )3 2
2 3
e x
x xdx
x
−
+∫
661. 4 2 1
xdx
x x+ +∫
662. 3
1 cos
sin
xdx
x
+
∫
663.
( )2
2
16
2 5
dx
x x− +∫
664.
( )3
2
8
1
dx
x +∫
665.
( )3
2
8
2
dx
x x+ +∫
666. 4
2 4
1
1
xdx
x x
−
+∫
667. ( )
( )
2
3
3 3 e sin
1
xx x x
dx
x
−+ +
+∫
668. tan x dx∫