∫ dx

x^2 X^3 =

−b

2 a^2 X−

2 b

a^3 X−

1

a^3 x+

3 b

a^4 ln|

X

x|

∫ x dx

Xn =

1

b^2

[ − 1

(n−2)Xn−^2 +

a

(n−1)Xn−^1

]

+C, n 6 = 1, 2

∫ x (^2) dx
Xn =
1
b^3
[
− 1
(n−3)Xn−^3 +
2 a
(n−2)Xn−^2 −
a^2
(n−1)Xn−^1
]
+C, n 6 = 1, 2 , 3
93.
∫ √
X dx= 32 bX^3 /^2 +C
94.
∫
x
√
X dx= 152 b 2 (3bx− 2 a)X^3 /^2 +C
95.
∫
x^2
√
X dx= 1052 b 3 (8a^2 − 12 abx+ 15b^2 x^2 )X^3 /^2 +C
96.
∫ √X
x dx= 2
√
X+a
∫ dx
x
√
X
97.
∫ √X
x^2 dx=−
√
X
x +
b
2
∫ dx
x
√
X
98.
∫ dx
√
X
=^2 b
√
X+C
99.
∫ x dx
√
X
= 32 b 2 (bx− 2 a)
√
X+C
100.
∫ x (^2) dx
√
X
= 152 b 3 (8a^2 − 4 abx+ 3b^2 x^2 )
√
X+C
101.
∫ dx
x
√
X






√^1
aln|
√
√X−√a
X+√a
|+C 1 , a > 0
√^2
−a
tan−^1
√
X
−a+C^2 , a <^0
102.
∫ dx
x^2
√
X
=−
√
X
ax −
b
2 a
∫ dx
x
√
X
103.
∫
xn
√
X dx=(2n+ 3)^2 bxnX^3 /^2 −(2n^2 na+ 3)b
∫
xn−^1
√
X dx
104.
∫ √X
xn dx=
− 1
(n−1)a
X^3 /^2
xn−^1 −
(2n−5)b
2(n−1)a
∫ √X
xn−^1 dx
105.
∫
xm−^1 Xndx=x
mXn
m+n+
an
m+n
∫
xm−^1 Xn−^1 dx+C
106.
∫ Xn
xm+1dx=−
Xn+1
ma xm+
n−m+ 1
m
b
a
∫ Xn
xmdx
Appendix C