Class notes Calculus II

NaturalLogA function
↳

↳
(n1
(n Xy
=




=
0

(nx +
/ny
jxx =
I
* +


(x - x =
( )
↳ (n Y = (nx -

1y ( z) (5 1) 5
- -
- =




↳ In xr = r .
Inx

&* dx Because * is continuous ,
we must
be able it
&
to integrate
In In 3x" Ind (n30 in xi) (1220in +
2))
- =




It d
-
-




In 304/nx- 1n2- 2 Iny It turns ...
out (nx =




In * >
-


In (x* +1) -
lux" - (n(x 1) -

E1nx * (lux] =

y (j+ at) = *


Inix)
-2)((kdx
+
(nxsini(ix) - (n(x" -2) =
mn(x)0
In x50 In sin (ix) Gln(x +




k
-




5 In x > 2 In sin(ix) -

isIn(x" -2)
:

[Inx](((x)) =
*

& [5(n x = (n(x *
1) - 4(n(x -



2)]
/luxoInl - In (x-2)"] (f(q(x)) f'(q(x)) = -

q(x)

"In In
T




* ((xix1))) = 3(x x)) ·
2x = 6x(x -1) *




Grupk f(x) = In x
x((n(g(x))) 4x) =
-

q(x) =
q(x) = ex

1




Y
39((n(3xx -


1) 134 = -
6x =
2
'

*x(ix] Ex (((nx)b) -((nx) *. k
C


·
= =




]
=




V
= * =
nux)

* [In(2x)] (2xx(x) 1) ) -




202(X 1)*. 3x -




54fxdx = za &
zi) 25
3x2




(4xsdx = 4 .
-

Ssinx dx = -cosXbc

,
,
,