(48)
Z
ln(ax + b) dx =
x +
b
a
ln(ax + b) - x, a 6=0
(49)
Z
ln(x
2
+ a
2
) dx = x ln(x
2
+ a
2
)+2a tan
-1
x
a
- 2x
(50)
Z
ln(x
2
- a
2
) dx = x ln(x
2
- a
2
)+ a ln
x + a
x - a
- 2x
(51)
Z
ln
(
ax
2
+ bx + c
)
dx =
1
a
√
4ac - b
2
tan
-1
2ax + b
√
4ac - b
2
-2x+
b
2a
+ x
ln
(
ax
2
+ bx + c
)
(52)
Z
x ln(ax + b) dx =
bx
2a
-
1
4
x
2
+
1
2
x
2
-
b
2
a
2
ln(ax + b)
(53)
Z
x ln
(
a
2
- b
2
x
2
)
dx = -
1
2
x
2
+
1
2
x
2
-
a
2
b
2
ln
(
a
2
- b
2
x
2
)
(54)
Z
(ln x)
2
dx =2x - 2x ln x + x(ln x)
2
(55)
Z
(ln x)
3
dx = -6x + x(ln x)
3
- 3x(ln x)
2
+6x ln x
(56)
Z
x(ln x)
2
dx =
x
2
4
+
1
2
x
2
(ln x)
2
-
1
2
x
2
ln x
(57)
Z
x
2
(ln x)
2
dx =
2x
3
27
+
1
3
x
3
(ln x)
2
-
2
9
x
3
ln x
6
