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СЕМИНАР №4. Áîäëîãî, äàñãàë.
110-146. Èíòåãðàë÷ëàõ õÿëáàð àðãààð áîä.
110. .
 dx
x 111. .
5
 x
dx
112. .
)
1
4
( 3
5
 −
+
− dx
x
x
x
113. .
)
3
2
(
 − dx
x
x 114. .
)
3
3
( 3
3
 + dx
x
x
115. .
)
2
( 2
 + dx
x
116. .
)
3
(
3
2

−
dx
x
x
x
117. .
2

+
dx
x
x
118. .
)
2
1
(
2
 + dx
x
x
119. .
1
2
3
2

−
+
dx
x
x
x
120. .
4

−
dx
e x
121. .
)
( 2

−
− dx
e
e x
x
122. .
3
 dx
x
123. .
2
3 2
  dx
x
x
124. .
16
2
 +
x
dx
125. .
25 2
 − x
dx
126. .
5
2
 −
x
dx
127. .
3
2
 −
x
dx
128. .
7
sin
 xdx 129. .
5
cos2
 x
dx
130. .
)
5
( 3
 + dx
x
131. .
2
1
 + dx
x 132. .
)
1
( 2

−
+ dx
x
e
e
x
x
133. .
2
cos
1
cos
1 2
 +
+
dx
x
x
134. .
sin
cos
2
cos
2
2
 dx
x
x
x
135. .
2
 xdx
tg 136. .
1 2
4
 +
dx
x
x
137. .
)
1
(
2
1
2
2
2
 +
+
dx
x
x
x
138. .
3
  dx
ex
x
139. .
)
2
3
( 5
 −
x
dx
140. .
)
3
7
(
5 6
 − dx
x 141. .
2
2 2
 + dx
x
x 142. .
1 2
 − dx
x
x
143. .
9
3
2
 + dx
x
x 144. .
sin
cos
3
 dx
x
x
145. .
ln
3
 dx
x
x
146. .
1 2
3
 +
dx
x
x
arctg
147-167. Îðëóóëàõ àðãààð áîä.
147. .
1
1
 +
+ x
dx
148. .
1
3
 −
x
dx
x
149. .
1
 +
x
dx
x
150. .
3
 − x
x
dx
x
151. .
1
 −
−
+ x
x
e
dx
e
152. .
1
5
4
 − x
xdx
153. .
ln
1 2
 − x
x
dx
154. .
4
 +
x
x
e
dx
e
155. .
2
1

−
x
dx
e x
156. .
)
2
1
(
2
 +
+
dx
x
e x
x
157. .
9
2
2
 +
x
x
dx
158. .
2
2
2
 − x
a
dx
x
159. .
8
2
 −
x
x
dx
160. .
1
4
2

+
x
dx
x
161. .
1
2
2

−
x
dx
x
162. .
1
1
2
 
+
−
x
dx
x
x
163-176. Õýñýã÷ëýí èíòåãðàë÷ëàõ àðãààð áîä.
163. .
)
5
2
( 3

−
− dx
e
x x
164. .
2
cos
 xdx
x 165. .
2

−
dx
xe x
166. .
2
sin
)
3
2
(
 − dx
x
x 167. .
ln
 dx
x
x
168. .
2
sin
)
8
5
( 2
 +
− xdx
x
x 169. .
ln
)
4
3
(
 − xdx
x
170. .
ln
 xdx
x 171. .
)
1
( 2
 + dx
e
x x
172. .
ln2
 xdx
173. .
)
1
(
ln
2
 +
dx
x
x
174. .
xarctgxdx 175. .
arccos
 xdx
176. .
cos
 nxdx
eax

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СЕМИНАР №4.pdf

  • 1. СЕМИНАР №4. Áîäëîãî, äàñãàë. 110-146. Èíòåãðàë÷ëàõ õÿëáàð àðãààð áîä. 110. .  dx x 111. . 5  x dx 112. . ) 1 4 ( 3 5  − + − dx x x x 113. . ) 3 2 (  − dx x x 114. . ) 3 3 ( 3 3  + dx x x 115. . ) 2 ( 2  + dx x 116. . ) 3 ( 3 2  − dx x x x 117. . 2  + dx x x 118. . ) 2 1 ( 2  + dx x x 119. . 1 2 3 2  − + dx x x x 120. . 4  − dx e x 121. . ) ( 2  − − dx e e x x 122. . 3  dx x 123. . 2 3 2   dx x x 124. . 16 2  + x dx 125. . 25 2  − x dx 126. . 5 2  − x dx 127. . 3 2  − x dx 128. . 7 sin  xdx 129. . 5 cos2  x dx 130. . ) 5 ( 3  + dx x 131. . 2 1  + dx x 132. . ) 1 ( 2  − + dx x e e x x 133. . 2 cos 1 cos 1 2  + + dx x x 134. . sin cos 2 cos 2 2  dx x x x 135. . 2  xdx tg 136. . 1 2 4  + dx x x 137. . ) 1 ( 2 1 2 2 2  + + dx x x x 138. . 3   dx ex x 139. . ) 2 3 ( 5  − x dx 140. . ) 3 7 ( 5 6  − dx x 141. . 2 2 2  + dx x x 142. . 1 2  − dx x x 143. . 9 3 2  + dx x x 144. . sin cos 3  dx x x 145. . ln 3  dx x x 146. . 1 2 3  + dx x x arctg 147-167. Îðëóóëàõ àðãààð áîä. 147. . 1 1  + + x dx 148. . 1 3  − x dx x 149. . 1  + x dx x 150. . 3  − x x dx x 151. . 1  − − + x x e dx e 152. . 1 5 4  − x xdx 153. . ln 1 2  − x x dx 154. . 4  + x x e dx e 155. . 2 1  − x dx e x 156. . ) 2 1 ( 2  + + dx x e x x 157. . 9 2 2  + x x dx 158. . 2 2 2  − x a dx x 159. . 8 2  − x x dx 160. . 1 4 2  + x dx x 161. . 1 2 2  − x dx x 162. . 1 1 2   + − x dx x x
  • 2. 163-176. Õýñýã÷ëýí èíòåãðàë÷ëàõ àðãààð áîä. 163. . ) 5 2 ( 3  − − dx e x x 164. . 2 cos  xdx x 165. . 2  − dx xe x 166. . 2 sin ) 3 2 (  − dx x x 167. . ln  dx x x 168. . 2 sin ) 8 5 ( 2  + − xdx x x 169. . ln ) 4 3 (  − xdx x 170. . ln  xdx x 171. . ) 1 ( 2  + dx e x x 172. . ln2  xdx 173. . ) 1 ( ln 2  + dx x x 174. . xarctgxdx 175. . arccos  xdx 176. . cos  nxdx eax