7. .
U=
dU=d(
, :
, , , .
U=x; dV=cosxdx.
dU=dx; V=
+cosx+C.
, :
8. .
.
U=cosx; dV=
dU=-sinxdx; V=
U=sinx; dV=
dU=cosxdx; V=
(1):
, : 2 , 2.
17.
1. | ||
2. | (x-1)cosx-sinx+C | |
3. | xarcsinx+ | |
4. |
1.
4.
1
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1. | 1. | 2 (1) . |
2. | . | |
3. | . | |
4. | , . | |
5. | , , . . | |
2. | 1. | . 3 4, . |
2. | . | |
3. | . . . | |
4. | , (n+1), n. | |
5. | . | |
3. | 1. | . |
2. | . | |
3. | . . . , 3. | |
4. | : | |
5. | , . . , 3. | |
5. | 1. | . |
2. | . . . | |
3. | . . |
2.
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1. | 1. | . 5, : t= , . |
2. | . | |
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2. | 2 1, . | |
3. | . . . |
3.
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3. | . |
4.
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3. | . . | |
2. | 1. | (n+1) (n-1). . . |
2. | , . . | |
3. | . |
|
|
5.
/ | ||
1. | 1. | . . 3 n=0. |
2. | ||
3. | . | |
, 1. . 3. | ||
2. | 1. | . |
2. | . -5cosx. . . | |
3. | . . . | |
4. | , 5. |
6
/ | ||
1. | 1. | . 2sinx. |
2. | . | |
3. | . sin2x=2sinxcosx, . . | |
2. | 1. | . -3sinx. . . |
2. | . |
7.
/ | ||
1. | 1. | . . . |
2. | . |
8.
/ | ||
1. | 1. | . . . |
2. | . | |
2. | 1. | . |
2. | . . . |
9.
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1. | 1. | . |
2. | . . . | |
3. | . . . | |
4. | . |
10.
/ | ||
1. | 1. | . . . |
2. | . . . | |
3. | . | |
4. | . |
11.
/ | ||
1. | 1. | . |
2. | dx dt, , (5+3) 3dx, , 3dx=dt, dx= , . . | |
3. | , . | |
4. | . | |
2. | 1. | . |
2. | dt. 5dx=dt; dx= . . . | |
3. | . | |
4. | . | |
3. | 1. | : . . . |
2. | . | |
4. | 1. | dt. . |
2. | . | |
3. | , -3. | |
5. | 1. | d(cosx)=-sinxdx. |
2. | n+1 n-1. | |
3. | . | |
6. | 1. | d(3-sinx)=-cosxdx. |
2. | . | |
3. | n+1 n-1. | |
7. | 1. | . |
2. | . | |
3. | . | |
8. | 1. | , , .. n=-5, n=-1. |
2. | . | |
3. | n=-5 n=5. |
12.
/ | ||
1. | 1. | . |
2. | , n=-1, n-1 n+1, 0. | |
3. | . | |
2. | 1. | . |
2. | ||
3. | . | |
3. | 1. | (n+1) (n-1). |
2. | . | |
3. | , . | |
4. | 1. | . |
2. | . | |
3. | . | |
5. | 1. | , , .. tgx=f(x), x. |
2. | . | |
3. | tgx . |
13.
/ | ||
1. | 1. | . |
2. | . | |
3. | . | |
2. | 1. | . |
2. | . , .. , . . | |
3. |
|
|
14.
/ | ||
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2. | . | |
3. | . | |
3. | 1. | , . . |
2. | . | |
3. | , . . |
15.
/ | ||
1. | 1. | , . . |
2. | . | |
3. | n=-2, , .. , , . . | |
2. | 1. | - , . . |
2. | . | |
3. | 1. | , . |
2. | . |
16.
/ | ||
1. | 1. | , . . |
2. | . 1 . | |
3. | . | |
2. | 1. | , . . |
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3. | . | |
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3. | , . |