(98)
Z
csc
2
ax dx = -
1
a
cot ax
(99)
Z
csc
3
x dx = -
1
2
cot x csc x +
1
2
ln | csc x - cot x|
(100)
Z
csc
n
x cot x dx = -
1
n
csc
n
x, n 6=0
(101)
Z
sec x csc x dx = ln | tan x|
Products of Trigonometric Functions and Mono-
mials
(102)
Z
x cos x dx = cos x + x sin x
(103)
Z
x cos ax dx =
1
a
2
cos ax +
x
a
sin ax
(104)
Z
x
2
cos x dx =2x cos x +
(
x
2
- 2
)
sin x
(105)
Z
x
2
cos ax dx =
2x cos ax
a
2
+
a
2
x
2
- 2
a
3
sin ax
(106)
Z
x
n
cos xdx = -
1
2
(i)
n+1
[Γ(n +1, -ix)+(-1)
n
Γ(n +1, ix)]
11
(107)
Z
x
n
cos ax dx =
1
2
(ia)
1-n
[(-1)
n
Γ(n +1, -iax) - Γ(n +1, ixa)]
(108)
Z
x sin x dx = -x cos x + sin x
(109)
Z
x sin ax dx = -
x cos ax
a
+
sin ax
a
2
(110)
Z
x
2
sin x dx =
(
2 - x
2
)
cos x +2x sin x
(111)
Z
x
2
sin ax dx =
2 - a
2
x
2
a
3
cos ax +
2x sin ax
a
2
(112)
Z
x
n
sin x dx = -
1
2
(i)
n
[Γ(n +1, -ix) - (-1)
n
Γ(n +1, -ix)]
(113)
Z
x cos
2
x dx =
x
2
4
+
1
8
cos 2x +
1
4
x sin 2x
(114)
Z
x sin
2
x dx =
x
2
4
-
1
8
cos 2x -
1
4
x sin 2x
(115)
Z
x tan
2
x dx = -
x
2
2
+ ln cos x + x tan x
(116)
Z
x sec
2
x dx = ln cos x + x tan x
12
