hoofdstuk 1
o 1 .
4
nrinxax
π
=
-
cox = co4 + (00 = 1 + 1 = 2
o
U 4323
-3
2) ta I
64 - 8 56
= C
=
- -
3 I 3 3 3 3 3
3) a = ex Y = ma -
ene = 0 -
1 =
4) =
5
x2 a
3/2
-312 2
. 4312
-2253
x 2 2 43
x ax = -
·
- -
318 4 3 3 3
255
E 2(55 n
2 125 - & A -
-
= = =
3 3 3
!u
&
5)
4
(3x2 4) ax r 3x 2 4
=
x + = au r =
+
U
O 6X
du = Ax
(3x 4)4 1
4)" 13 0 +
12
(3
&
.
+ -
.
- =
Y o 4
7444 2401 256 I 715
-
> 62145
-
-
- - = =
6 4 4 Y U U 8
6)je
π/2
ein 000 (0 Ca +(2 + (a π13 0 + 112
=
-
-
= = =
+ 13
2)
a
=
bgtex =
6glan4
-
bgtan
-
1 = π(4 + π(4 = 2π(4 = T
-
1
x
8 2Een u
4 2
2
π2
in dt - au =
-
coor r =
a
U Y
-
T T
2
πtE 2π
de
-E car du
-
=
-
I
U U
+ 1)2
2
-( cπ2 I
+
π .
πt de
co
-
-
H U 2
2 T 2 2 +
2 2
i
42
-
-
Co + Co = t -
T 4 H Th
T/2 π/2
π/2
2
9) in xdx = (vinx .
sinxax =
f(4 -
Co x) .
sin x dx sin2x +
(0 x = 1
TT12
sin2 x 2002 x
-
-
T12 1
π12
-
=
-ik - 02 du =
-
-
T/2
/**au +
-
π/2
een r
du
= CO0X
= -sinxdx
π/2 3 T12 π/2
-- &
T/2
-
t
3
U
-- coox + CO23X
π12 3
T/2
-
-
casπ (6 +12 Ca T
co-
-
- + t
-
- 0 + 0 + G -O - O
I 3 3
, 2 tan a atana
2 tan a
+(2)
S ·
o dX
(a /2
18)
xe
E
, =
22 + x
&
-
" betan G
&tana e
-"
>
-
Ogtan by tan
(0)
-1 bgtan(tana) -
4 bgtan =
2 -.
L
anax & -
o =
Ggan =
Ggan-6geino =
5 e
T
as) maxis = =- =
Egtan -
I
!glan- , =
π
betan -
d 0
· -
-
O U
3
n3(x)ax
O O 3
f b 2 + -
0 ( 1)
-202 3
-
=
-
xax + < ax = =
-
S 2
G
= 0
!
+ +
9 -
0 =
1
T/2 T/2 π/2
14) sin(x)dx ein( x)ax sin ax Pan ax S
+
x x +
, =
πI2
- cox + -
Cox
O
-cas 0-CC0 + 17) -
C60 T12 + 1000
,
-
- 1 + 1 -
0 + 1 = 3
2
153x + xax
= x (1 + x9)ax
=
9(xa + x ax =
P x x + x ax
+S x a + x x
-- u au
+ ax V
du
= 1 +
=
x2
2xdx
-90'
O 2
2 -312 U 3/2
laa I
+
-
du = t
2 3/2 2 3/2 G
-
I
0 2
-
I (1 + x2/3/2 +
1 ca + xa)3/2
2 3/2 2 312
-
I O
I 1312 2312 16312 4312
t
-
-
D
E
23/2 3/2 S 3/2 3/2
2 2
- + 125
-
8 2 4
3
2 2
-
-4 2 t
105-3
2
-
5 +
2 2 +
355 % =
35 +
22
, canBa
16)
Fan x (6 , Be
(2 , (2) =
Ggtanx ama =
bgtan(tanB) -
6 gtan(tana) =
B
17 / (x + 1) ax
=, x + 2x + dax
=
x ax
+, 2x ax
+Sax
-
4' + 2x + x'
3
-
I -
I
H 23 H
13
- 1)
5 ' !
2 2
+ 4
- -
- + = + + +
5
G 20 56
3 3
30
- +
23 + 2 = +
3 =
15
t
3
t
15
=
15
n8)( = zat 227
(2)
2
2)da tan a- + t(2t 7) ↳
+
+ +
-
-
-
2 2
t
++
4 ta 372
E 2t2 + -5
2
-
- + = -
2 q 2
"
e⑩ ax-Ya
e
n9) x "
2
x Fax
d x"
is
x
ax ax
=
= =
x* 2
L
3
-(n 2 4) 13 1 A
n
+
-
+
-
-
=
-
3 ..3
8
en 5
1 +1 -N na
- A
-
1
-
- + -
t - = -
- 3 24 24 24 24
20)9(x 3x 3x 6x3
- 6
(x x )dx
y
-
2
x
+
2 ax ax x t
+
+
= =
=
I
333
-
-6. - +
6
3
-
3 = I
3
t
216
3
-
27
3
I
-3 72 9
= 3 63 63 H
-
- +
+ =
+
+ =
+
6
Sao 3 adu =su du
2
·f
-2
21) - =
a
↓
u = 2x + 1
en au = 2dx
2 2
2 2
1)
-
1 (213
- -
(2x + 1 5 -
+
<C
= ⑨}
L -
I 2 -
L -
2
-
113
-2
(113)
225 Sae
I 1 I I 9 1 -
=
- -
- t ↳
-
N
= =
2 so -
2 2 50 2 250
=
& 18 =
3
, 22
,
3)x -
'
,
ax = x" ax
= x ax =
x
312
3/25
M
- x
2/3n
2135
-
3 53 - n -
33
se 1
3325 3325
105 3 + 102
5
3 +
-
- -
- =
3
23) ! i
de
-891) + 1
du =
2Ju -
2 de u
du
=
'
=
t +
t
1
-
12
I
-
I
24
-2 Yuau-2) du +
2 en t
t
=
= W
(u
-
-
1
1)2
-
20 -
au +
2 ens
I
1 1)'
2
1)
-
2(t + -
2 + + + 2m)t +
5
1
24(5 2)5 1)
+
-
-
-
4 + + + 2en2 -
2e 1
L
15 19 4 (5 1)
,
4 + 42n2 42n5 + 1
{
L
+
+
+
-
- -
/
2 D & R
-
- 4 -
(5 + 25 + 2) -
8 + 45 + 4 + 42n2 -
42n5 + 1
-
=
1 -
5 -
25 -
2 -
8 + 45 + 4 + 2(6 -
42n5 + 1
1
-
7 + 25 -
425 +
2
aus" ax = Ve
een du =
+ (ide du u
du
=
=
4x
4x
+ 1
4x 1
-" de
= u -
1
au = de x =
I
jusaut j iede 2 den
- du =
-
+ n
U512
-j u
du-2-312 + H du &u e
4
VII "2 112 4 312
-
-
I -
= - V t
64 112 -112 -
3/2
O G O
o 1 .
4
nrinxax
π
=
-
cox = co4 + (00 = 1 + 1 = 2
o
U 4323
-3
2) ta I
64 - 8 56
= C
=
- -
3 I 3 3 3 3 3
3) a = ex Y = ma -
ene = 0 -
1 =
4) =
5
x2 a
3/2
-312 2
. 4312
-2253
x 2 2 43
x ax = -
·
- -
318 4 3 3 3
255
E 2(55 n
2 125 - & A -
-
= = =
3 3 3
!u
&
5)
4
(3x2 4) ax r 3x 2 4
=
x + = au r =
+
U
O 6X
du = Ax
(3x 4)4 1
4)" 13 0 +
12
(3
&
.
+ -
.
- =
Y o 4
7444 2401 256 I 715
-
> 62145
-
-
- - = =
6 4 4 Y U U 8
6)je
π/2
ein 000 (0 Ca +(2 + (a π13 0 + 112
=
-
-
= = =
+ 13
2)
a
=
bgtex =
6glan4
-
bgtan
-
1 = π(4 + π(4 = 2π(4 = T
-
1
x
8 2Een u
4 2
2
π2
in dt - au =
-
coor r =
a
U Y
-
T T
2
πtE 2π
de
-E car du
-
=
-
I
U U
+ 1)2
2
-( cπ2 I
+
π .
πt de
co
-
-
H U 2
2 T 2 2 +
2 2
i
42
-
-
Co + Co = t -
T 4 H Th
T/2 π/2
π/2
2
9) in xdx = (vinx .
sinxax =
f(4 -
Co x) .
sin x dx sin2x +
(0 x = 1
TT12
sin2 x 2002 x
-
-
T12 1
π12
-
=
-ik - 02 du =
-
-
T/2
/**au +
-
π/2
een r
du
= CO0X
= -sinxdx
π/2 3 T12 π/2
-- &
T/2
-
t
3
U
-- coox + CO23X
π12 3
T/2
-
-
casπ (6 +12 Ca T
co-
-
- + t
-
- 0 + 0 + G -O - O
I 3 3
, 2 tan a atana
2 tan a
+(2)
S ·
o dX
(a /2
18)
xe
E
, =
22 + x
&
-
" betan G
&tana e
-"
>
-
Ogtan by tan
(0)
-1 bgtan(tana) -
4 bgtan =
2 -.
L
anax & -
o =
Ggan =
Ggan-6geino =
5 e
T
as) maxis = =- =
Egtan -
I
!glan- , =
π
betan -
d 0
· -
-
O U
3
n3(x)ax
O O 3
f b 2 + -
0 ( 1)
-202 3
-
=
-
xax + < ax = =
-
S 2
G
= 0
!
+ +
9 -
0 =
1
T/2 T/2 π/2
14) sin(x)dx ein( x)ax sin ax Pan ax S
+
x x +
, =
πI2
- cox + -
Cox
O
-cas 0-CC0 + 17) -
C60 T12 + 1000
,
-
- 1 + 1 -
0 + 1 = 3
2
153x + xax
= x (1 + x9)ax
=
9(xa + x ax =
P x x + x ax
+S x a + x x
-- u au
+ ax V
du
= 1 +
=
x2
2xdx
-90'
O 2
2 -312 U 3/2
laa I
+
-
du = t
2 3/2 2 3/2 G
-
I
0 2
-
I (1 + x2/3/2 +
1 ca + xa)3/2
2 3/2 2 312
-
I O
I 1312 2312 16312 4312
t
-
-
D
E
23/2 3/2 S 3/2 3/2
2 2
- + 125
-
8 2 4
3
2 2
-
-4 2 t
105-3
2
-
5 +
2 2 +
355 % =
35 +
22
, canBa
16)
Fan x (6 , Be
(2 , (2) =
Ggtanx ama =
bgtan(tanB) -
6 gtan(tana) =
B
17 / (x + 1) ax
=, x + 2x + dax
=
x ax
+, 2x ax
+Sax
-
4' + 2x + x'
3
-
I -
I
H 23 H
13
- 1)
5 ' !
2 2
+ 4
- -
- + = + + +
5
G 20 56
3 3
30
- +
23 + 2 = +
3 =
15
t
3
t
15
=
15
n8)( = zat 227
(2)
2
2)da tan a- + t(2t 7) ↳
+
+ +
-
-
-
2 2
t
++
4 ta 372
E 2t2 + -5
2
-
- + = -
2 q 2
"
e⑩ ax-Ya
e
n9) x "
2
x Fax
d x"
is
x
ax ax
=
= =
x* 2
L
3
-(n 2 4) 13 1 A
n
+
-
+
-
-
=
-
3 ..3
8
en 5
1 +1 -N na
- A
-
1
-
- + -
t - = -
- 3 24 24 24 24
20)9(x 3x 3x 6x3
- 6
(x x )dx
y
-
2
x
+
2 ax ax x t
+
+
= =
=
I
333
-
-6. - +
6
3
-
3 = I
3
t
216
3
-
27
3
I
-3 72 9
= 3 63 63 H
-
- +
+ =
+
+ =
+
6
Sao 3 adu =su du
2
·f
-2
21) - =
a
↓
u = 2x + 1
en au = 2dx
2 2
2 2
1)
-
1 (213
- -
(2x + 1 5 -
+
<C
= ⑨}
L -
I 2 -
L -
2
-
113
-2
(113)
225 Sae
I 1 I I 9 1 -
=
- -
- t ↳
-
N
= =
2 so -
2 2 50 2 250
=
& 18 =
3
, 22
,
3)x -
'
,
ax = x" ax
= x ax =
x
312
3/25
M
- x
2/3n
2135
-
3 53 - n -
33
se 1
3325 3325
105 3 + 102
5
3 +
-
- -
- =
3
23) ! i
de
-891) + 1
du =
2Ju -
2 de u
du
=
'
=
t +
t
1
-
12
I
-
I
24
-2 Yuau-2) du +
2 en t
t
=
= W
(u
-
-
1
1)2
-
20 -
au +
2 ens
I
1 1)'
2
1)
-
2(t + -
2 + + + 2m)t +
5
1
24(5 2)5 1)
+
-
-
-
4 + + + 2en2 -
2e 1
L
15 19 4 (5 1)
,
4 + 42n2 42n5 + 1
{
L
+
+
+
-
- -
/
2 D & R
-
- 4 -
(5 + 25 + 2) -
8 + 45 + 4 + 42n2 -
42n5 + 1
-
=
1 -
5 -
25 -
2 -
8 + 45 + 4 + 2(6 -
42n5 + 1
1
-
7 + 25 -
425 +
2
aus" ax = Ve
een du =
+ (ide du u
du
=
=
4x
4x
+ 1
4x 1
-" de
= u -
1
au = de x =
I
jusaut j iede 2 den
- du =
-
+ n
U512
-j u
du-2-312 + H du &u e
4
VII "2 112 4 312
-
-
I -
= - V t
64 112 -112 -
3/2
O G O
