Begin2.DVI

∫ dx

x^2 X^3 /^2 =−

√

X

a^4 x+

x

a^4

√

X

+C

∫ dx

x^3 X^3 /^2 =−

1

2 a^2 x^2

√

X

+^3

2 a^4

√

X

− 23 a 5 ln|a+

√

X

x |+C

Integrals ContainingX=x^3 +a^3

∫ dx

X =

1

6 a^2 ln|

(x+a)^3

X |+

√^1

3 a^2 tan

− 1

( 2 x−a

√

3 a

)

+C

∫ x dx

X =

1

6 aln|

X

(x+a)^3 |+

√^1

3 a

tan−^1

(

(^2) √x−a
3 a
)
+C
321.
∫ x (^2) dx
X =
1
2 ln|X|+C
322.
∫ dx
xX=
1
3 a^3 ln|
x^3
X|+C
323.
∫ dx
x^2 X=−
1
a^2 x−
1
6 a^4 ln|
X
(x+a)^3 |−
√^1
3 a^4
tan−^1
(
2 x√−a
3 a
)
+C
324.
∫ dx
X^2 =
x
3 a^3 X+
1
9 a^5 ln|
(x+a)^3
X |+
2
3
√
3 a^5
tan−^1
( 2 x−a
√
3 a
)
+C
325.
∫ x dx
X^2 =
x^2
3 a^3 X+
1
18 a^4 ln|
X
(x+a)^3 |+
1
3
√
3 a^4
tan−^1
( 2 x−a
√
3 a
)
+C
326.
∫ x (^2) dx
X^2 =−
1
3 X+C
327.
∫ dx
xX^2 =
1
3 a^2 X+
1
3 a^6 ln|
x^3
X|+C
328.
∫ dx
x^2 X^2 =−
1
a^6 x−
x^2
3 a^6 X−
4
3 a^6
∫ x dx
X
329.
∫ dx
X^3 =
1
54 a^3
[
9 a^5 x
X^2 +
15 a^2 x
X + 10
√
3 tan−^1 (^2 x√−a
3 a
) + 10 ln|x+a|−5 ln|x^2 −ax+a^2 |
]
+C
Integrals containingX=x^4 +a^4
330.
∫ dx
X =
1
4
√
2 a^3
ln| X
(x^2 −
√
2 ax+a^2 )^2
|−^1
2
√
2 a^3
tan−^1
(√
2 ax
x^2 −a^2
)
+C
331.
∫ x dx
X =
1
2 a^2 tan
− 1
(x 2
a^2
)
+C
332.
∫ x (^2) dx
X =
1
4
√
2 a
ln| X
(x^2 +
√
2 ax+a^2 )^2
|−^1
2
√
2 a
tan−^1
(√
2 ax
x^2 −a^2
)
+C
333.
∫ x (^3) dx
X =
1
4 ln|X|+C
334.
∫ dx
xX=
1
4 a^4 ln|
x^4
X|+C
335.
∫ dx
x^2 X=−
1
a^4 x−
√^1
24 a^5
ln|(x
(^2) −√ 2 ax+a (^2) ) 2
X |+
1
2
√
2 a^5
tan−^1
(√
2 ax
x^2 −a^2
)
+C
336.
∫ dx
x^3 X=−
1
2 a^4 x^2 −
1
2 a^6 tan
− 1
(x 2
a^2
)
+C
Appendix C