THE NATURAL LOGARITHM
187
23.21 Find
Use Problem 23.20:
23.22
Find J tan x dx.
Use Problem 23.20:
Since
— ln|cos^|- =
In (|cos *!-') = In (|secjr|), the answer can be written as In |sec x\ + C.
In Problems 23.23-23.26, use logarithmic differentiation to find y'.
23.23
In y = In x3 + In (4 - x2)1'2 = 3 In x + \ In (4 - x2). By implicit differentiation,
Hence,
23.24
In y = \n(x- 2)4 + In (x + 5)1'3 - In (x2 + 4)"2 = 4 In (x - 2) + ! In (x + 5) - \ In (x2 + 4). By implicit differentiation,
So,
23.25
In y = In (x2 - I)1'2 + In (sin x) - In (2x + 3)4 = | In (x2 - 1) + In (sin x) - 4 In (2x + 3). Hence,
Hence,
23.26
In (*-!)].
In
In y =
Hence,
So,
In Problems 23.27-23.34, express the given number in terms of In 2 and In 5.
23.27
In 10.
In 10 = In (2 • 5) = In 2 + In 5.
23.28
ln|.
In |=ln2"
1 = -In 2.
dx=l\n \3x
2 + 1| + C.
dx =
/ tan x dx =
dx=dx = -In |cos x\ + C.