186
CHAPTER 23
23.11
23.12
Then
Then
23.13
Let
Then
Then
23.14
Let
[Compare Problem 23.6.]
23.15
Let
Then
23.16
23.17
23.18
Let u - tan x, du = sec
2 x dx. Then
Let u = \-Vx, du = -(l/2Vx)dx. Then
23.19
23.20 Show that
Let M = g(x), du = g'(x) dx. Then
ln| M l + C = \\n\lx-2\ + C.
Let u = 7x-2, du=l dx.
dx.
dx.
du= %
dx =
Let u = x
4 — 1, du=4x*dx.
J cot x dx.
u = sin x, du = cos x dx.
J cot x dx =
dx =
dw = ln|w| + C = ln|sinA-| + C
w = In x, du = dx.
dx =
rf« = ln|w| + C = ln(|lnjc|)+C.
w = 1 — sin 2x, du = —2 cos 2x dx
dx =
du = -{ \n\u\ + C= -| In|l-sin2x| + C
rfx = 3 J A2 rfx + 2
dx - 3 J x^
3 dx = jc
3 + 2 In |*| + l^r"
2 + C.
dx =
du = In |M| + C = In |tan x\ + C
dx.
dx = -2
du = -2 In |«| + C = -2 In |1 - Vx\ + C
dx.
dx =
dx={(lnx)
2 + C.
dx = \n\g(x)\ + C.
du = ln\u\ + C = \n\g(x)\ + C
dx =
(In*)
du = | In \u\ + C = | In \x
4 - 1| + C.
dx =