(68)
Z
e
-ax
2
dx =
√
π
2
√
a
erf
(
x
√
a
)
(69)
Z
xe
-ax
2
dx = -
1
2a
e
-ax
2
(70)
Z
x
2
e
-ax
2
dx =
1
4
r
π
a
3
erf(x
√
a) -
x
2a
e
-ax
2
Integrals with Trigonometric Functions
(71)
Z
sin ax dx = -
1
a
cos ax
(72)
Z
sin
2
ax dx =
x
2
-
sin 2ax
4a
(73)
Z
sin
3
ax dx = -
3 cos ax
4a
+
cos 3ax
12a
(74)
Z
sin
n
ax dx = -
1
a
cos ax
2
F
1
1
2
,
1 - n
2
,
3
2
, cos
2
ax
(75)
Z
cos ax dx =
1
a
sin ax
(76)
Z
cos
2
ax dx =
x
2
+
sin 2ax
4a
(77)
Z
cos
3
axdx =
3 sin ax
4a
+
sin 3ax
12a
8