(20)
Z
x
√
x - a dx =
2a
3
(x - a)
3/2
+
2
5
(x - a)
5/2
, or
2
3
x(x - a)
3/2
-
4
15
(x - a)
5/2
, or
2
15
(2a +3x)(x - a)
3/2
(21)
Z
√
ax + b dx =
2b
3a
+
2x
3
√
ax + b
(22)
Z
(ax + b)
3/2
dx =
2
5a
(ax + b)
5/2
(23)
Z
x
√
x ± a
dx =
2
3
(x ∓ 2a)
√
x ± a
(24)
Zr
x
a - x
dx = -
p
x(a - x) - a tan
-1
p
x(a - x)
x - a
(25)
Zr
x
a + x
dx =
p
x(a + x) - a ln
√
x +
√
x + a
(26)
Z
x
√
ax + b dx =
2
15a
2
(-2b
2
+ abx +3a
2
x
2
)
√
ax + b
(27)
Z
p
x(ax + b) dx =
1
4a
3/2
h
(2ax + b)
p
ax(ax + b) - b
2
ln
a
√
x +
p
a(ax + b)
i
(28)
Z
p
x
3
(ax + b) dx =
b
12a
-
b
2
8a
2
x
+
x
3
p
x
3
(ax + b)+
b
3
8a
5/2
ln
a
√
x +
p
a(ax + b)
(29)
Z
√
x
2
± a
2
dx =
1
2
x
√
x
2
± a
2
±
1
2
a
2
ln
x +
√
x
2
± a
2
3
