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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∫
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