Appendix A
A Short Table of Integrals
(1)
du
a 2 + u 2 =
1
a
arctan
u
a
+ C
(2)
du
√
u 2 ± a 2
= ln |u +
√
u 2 ± a 2 | + C
(3)
√
u 2 ± a 2 du =
u
2
√
u 2 ± a 2 ±
a 2
2
ln |u +
√
u 2 ± a 2 | + C
(4)
u 2 du
√
u 2 ± a 2
=
u
2
√
u 2 ± a 2 ∓
a 2
2
ln |u +
√
u 2 ± a 2 | + C
(5)
du
u
√
u 2 + a 2
= −
1
a
ln
a +
√
u 2 + a 2
u
+ C
(6)
du
u
√
u 2 − a 2
=
1
a
sec
−1 u
a
+ C
(7)
du
√
a 2 − u 2
= arcsin
u
a
+ C
(8)
√
a 2 − u 2 du =
u
2
√
a 2 − u 2 +
a 2
2
arcsin
u
a
+ C
(9)
u 2
√
a 2 − u 2
du = −
u
2
√
a 2 − u 2 +
a 2
2
arcsin
u
a
+ C
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