(10)
Z
x
a
2
+ x
2
dx =
1
2
ln |a
2
+ x
2
|
(11)
Z
x
2
a
2
+ x
2
dx = x - a tan
-1
x
a
(12)
Z
x
3
a
2
+ x
2
dx =
1
2
x
2
-
1
2
a
2
ln |a
2
+ x
2
|
(13)
Z
1
ax
2
+ bx + c
dx =
2
√
4ac - b
2
tan
-1
2ax + b
√
4ac - b
2
(14)
Z
1
(x + a)(x + b)
dx =
1
b - a
ln
a + x
b + x
,a 6= b
(15)
Z
x
(x + a)
2
dx =
a
a + x
+ ln |a + x|
(16)
Z
x
ax
2
+ bx + c
dx =
1
2a
ln |ax
2
+bx +c|-
b
a
√
4ac - b
2
tan
-1
2ax + b
√
4ac - b
2
Integrals with Roots
(17)
Z
√
x - a dx =
2
3
(x - a)
3/2
(18)
Z
1
√
x ± a
dx =2
√
x ± a
(19)
Z
1
√
a - x
dx = -2
√
a - x
2