Begin2.DVI

∫ x (^3) dx
X^2 =
a^2
2 X+
1
2 ln|X|+C
285.
∫ dx
xX^2 =
1
2 a^2 X+
1
2 a^4 ln|
x^2
X|+C
286.
∫ dx
x^2 X^2 =−
1
a^4 x+
x
2 a^4 X+
3
4 a^5 ln|
a+x
a−x|+C
287.
∫ dx
x^3 X^2 =−
1
2 a^4 x^2 +
1
2 a^4 X+
1
a^6 ln|
x^2
X|+C
288.
∫ dx
Xn=
x
2(n−1)a^2 Xn−^1 +
2 n− 3
2(n−1)a^2
∫ dx
Xn−^1
289.
∫ x dx
Xn =
1
2(n−1)Xn−^1 +C
290.
∫ dx
xXn=
1
2(n−1)a^2 Xn−^1 +
1
a^2
∫ dx
xXn−^1
Integrals containing the square root ofX=a^2 −x^2 withx^2 < a^2
291.
∫ √
X dx=^12 x
√
X+a
2
2 sin
− 1 x
a+C
292.
∫
x
√
X dx=−^13 X^3 /^2 +C
293.
∫
x^2
√
X dx=−^14 xX^3 /^2 +^18 a^2 x
√
X+^18 a^4 sin−^1 xa+C
294.
∫
x^3
√
X dx=^15 X^5 /^2 −^13 a^2 X^3 /^2 +C
295.
∫ √X
x dx=
√
X−aln|a+
√
X
x |+C
296.
∫ √X
x^2 dx=−
√
X
x −sin
− 1 x
a+C
297.
∫ √X
x^3 dx=−
√
X
2 x^2 +
1
2 aln|
a+
√
X
x |+C
298.
∫ dx
√
X
= sin−^1 xa+C
299.
∫ x dx
√
X
=−
√
X+C
Appendix C