Evidence iii

Evidence iii
1 f(x) = In (3x2) 2. .
dA v 13
= . f(x)
3 =
2x3Sin(5x)
=
10
6x dt v =
312(t)
2
3x2
f(x) =
2x3(sin(Sx) + SinSx(2x3) ,

v = 3(s)2(10) 1 7 5 .
f'(x) = 2 x3(5cos(5x) +
Sin(5x)(6x3)
=
f'(x) = 10x 3
cos5x + 6x2 Sin 5x

Sen(tx)
4 .

y
= 5xe5x S .

y(x)
=

X
6 .
V = 3 + 2(t)

(7cos(7x))
f((x)
* Sen(7x)
3(3)2
-

=
Sx(Se3x) + es x (s) f(x) = v =

X2
>
-

f'(x)25xeSx + SeSx
>
-
f(x) =
(SeSx)(x + 1) >
-
f'(x) =
+ cos(7x) + Sen(tx) v =
3
X X2

7 2(3x2 10x 6) e5x 8x 8

. f(x) 3xz 9 f(x)
2
-

+ + 2xS 4 = 2x + x
-
=
+
y
. = - -
-
.

f(x) S3x2 25xs + S4

5(x 2(x
=

Sx
-

-
+ - 2

10x 6)
f'(x) 18)2(3x2
+
-

=
(6x +

f(x) = x3 -

* + 4x + c f(x) =
" -
x2 -

y + c

8x
(n(21 Se5x
-

10 .
x2 -
- + 7x -
4 17 .
f'(x) = 4x3 12 f(x)
.
= 5x4 -
6x + 5

f(x) x4
f(x) =
* -
5(n(x) + -
4x + c = + C f(x) = xS -
2x3 + 5x + C

f(x) 3( z
. J (E -ydx
-

13 14
-

=
x
+
2x + 2x + 4 Is
.
dx .

f(x) =
y -

y + x2 + x + c
- 2x3 12
S6x
2 + Sx" 10x 2
+
-

, gx , -
-

Syn (2x
S(5x)3dx
(6x4 4x4dx
17 18
16
5dx 19 +

by
-
. . . .

X3

In(x1 + C
>
-

15x In (x31 C

3y
> +

estet
-

+ C
 ((x = (3) ¢ X
/-
20 21 +
.

E3dx .

S2x * 12 -
x3 +
= +2 +
>
-
X
3
+
2 +
2x4/2
4x 2 -
- 4k +
5ks + c
a

22 .
S? St de 23 . S ."Cos(x)dx
=
15
s(5)2 5(0)2 125 [sin(x)] sin(π) -
Sin(0) =
0 -
0 =
0
-
= >
-
62 . S
2 2 2

24 .
S [ (T2
.
+ 7x)dx 25 .
S : (x-212dx
Litax + 2) - (-i) (2 2) 310-273
([3] ? -
-
-
3
21
= -

=
3 3

42x
20) ,
x2
>
-

(2In(x)" +> (2In(4)-(21/11] + PIn121 +

2 7725
.

5(esx
eSx 1dx
.
1
c) 28
+
-

27
-

+ + +
.
x + + c

1
29 .

/* >
- (n(x =
01 + c
30 .
(42x(x -
2(n(4)
:
42x + c
+ + C

Jedx-le
31
g3xdx + Inix-x +
32 .

Sin S x
7

57xdx sinzi +* ((e" 5( "dx ex ex + + c

-

c
-
+
33 + - 34 + + +
:
+
. + .
in(s)

esx
Je
S
((e Sy
-

35 12)dx 12x 36 f(x) 2(os(x) 3Sin(x)

-

+ +
-
+ + c +
-
+ 12x + C = -
-

5
. .

>
-
-
2sin(x) + 3cos(x) + C

37 . SSec (2x) (Sec (2x) -

Tan(2x))dx -> tan(2x) - E sec(2x) + c

38 JSen (10x1dx +
-

Tocos(10x) + > 39 . Jesen (3x)(os(3x)dx + +esin(3x) + c

4) 0 .( 4 Sec2 (4t) dt + tan (4t) + C 4) (5 Sen (5 +)dt + -

cos (St) + C

42 .
Scos(4x) dx
+ <sin(4x) +
Sin4x) + c 13
. Sen (8x)dx +
cos(8x) +
cs(8x)
E
+ c
44
/bdx 45Sx2xsd-2x3s
.

+
3x +

S3x2(x3-9)"2dx SIn
vinv) -
46 .
>
-
Sustitucion de "U" 47 . 3xdx 1 Sin(v)dv =

x + c = x .
((n(3x) + 1 + C

x(n(3x) -
x + Sin(3x)dx -

x((n(3x) - 1) + c

18 (5x)
J Sin(5x (5x
dx - Exsin(x cos
+

Sin dx
&Sin
.
-

25

49 .
a : Sxe = dx < dx = xe
-X
-
e7x
+
(7x -
1)e7x
+ C
7 4a 49

So .
Sx Sen (5x)dx >
- bx = x -in(x)
2
-
xx

4
>
-
X2 .
(2 , n(x) x)
4
.

+ c
#
colos124
Sx(n(x)dx
en
cos(5x)
g)
51 + (x = -
X
.
cos(v)dv =
+ C
S

32(xz 3x - + 2
¢ x -
fx2 3x -
+ 2dx)(n((x
-
21) -
(n(x -
2x +

S)) 5)) 21)

(n((x 2((x 5(n((x + S(n((x
+

(x
+
-

19
- -

+
53 .
+ c
2
x2 + 3x -
18

9
54 (n((x + b) + 3(n((x b))
D
-

> + c
.

55 .
Scot2(x)dx 56 . Ssenz (2x)dx 57 .
Scos2(x)dx

S(cs2x -
1)bx S(t Ecos4x)dx -

Si + cos2X dx

Scsc2xdx -
Sdx (dx Scos4xdx -
w = 2x

4X
dw = 2dx
v = X v =

dv = dx du = 4dx =d

Jax-
Scsc2vdv-Sax
Sex + Scoswow
-
cotx -
x +
C odr
[X +
Esen2x + c

X - Sen 4x + C
55 .
Scot2(x)dx 56 . Ssenz (2x)dx 57 .
Scos2(x)dx

S(cs2x -
1)bx S(t Ecos4x)dx
-

Si + cos2X dx

Scsc2xdx -
Sdx (dx Scos4xdx
-
w = 2x

4X
dw = 2dx
v = X v =

dv = dx du = 4dx =d

Jax-
Scsc2vdv-Sax
Sex + Scoswow
-
cotx -
x +
C odr
[X +
Esen2x + c

X - Sen 4x + C

= v"
9
2
58 Scos(6x) cos(3x)dx 59
+ c

-
x
- .
=
. .

DX
m = 6n = 3 81 -
x2

sen(6 + 3)x sen(b -

3)x =
81 x2
-v"2 + C

fr'
+ c v -

+ -
do
2(6 3) 2(6 3)
+
(81 x2)
-

dv = -
2xdx -
- +
C

-
senax Sen3x
181
- + + C
Cu xx x2 + c
- -
-
=
18 6

Ju S facosudn
60
-secrd JX
asecztanzaz 6).
.

= = = =
Jc-
a COS 2
a tanz
= In/seczttanz + C

= In1 sec Carsec ( * )) + tan Carsec(5) + c =

arssen + c

62 f(x) = x2 f(x) =
16 63 f(x) =
(x 2(2 ; f(x) = 4
y
-
. .

A =
S! (4 -
(x2 4x + 4) d X A =
5 ((4)3 10(3) +
2 [(4)2 1012]
-

Aj(16-x
-
-

A =
128
-

5(128) A= S (
"
-
xz + 4x -
4)dx A
-
=
5((4) + 2(16)
128
A =
128 -

3
A =
f( -
x2 + 4x)dx A = -

6 + 32
A = 16(ax -
(x2dx A =
256 A -
= Sx2dx + 4)dx
-2
A =
16x -
( - )S "
.
3
A -
=
(x + 4
X2
A = 32u2
2 3
4

A = 16(4 -
1 -
4)) -
-[(4)3 -
1 -
4(3) A =
-
5X3 +
2x20

64 =
x (0 4] 65 f(x) =
x2 -
8x (0 4]
y , ,
.
.

#S5(x)2dx =
i)"(x -
8x)dx = i ( (1413 -
1013) -

4((4)2 -

1012]
#(x 2dx = +( - ) = (x2dx -
8(xdx
=
((4(2 (0)) =
16 +
= -

120 =
32
=-
-

3 X24
8
2 g
6
6 f(x) =
19 x x = 2 x = 1 f'(x) = 19

S c
.
1 + 11912dx

S1 + 361 dx

(1362 1
. 362 ! (x =
362 x
! =
362( -
2 -
x =
362 -
3) = -
3362

67 68 2x2 21 =

1y + 6
dy cos (
-
.
.

dy = cos(5x)dx 69
Soy =
Scos(5x) d x
.

-:2x
cy =
2x--
y
= 5Scoswdw
dy =
2x
-
E +
z)dx
y
= -sen(5x) c +

Say = 2 (xc(x + (dx

y
=
2(x) + x + c

= x2 + x + C
y

72 3

.dy
-
3

dy = 5 dx
Soy =
5(xdx
y
=
5) + c

y
=
5x2 + c