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Appendix C

Table of Integrals

Z Z
udv = uv − vdu

Z 0
f (x)
dx = log f(x)
f(x)
Z 0
f (x) p
dx = f(x)
p
2 f(x)
Z α+1
x
α
x dx = for α 6== −1
α + 1
Z
1
dx = log x
x
Z ax
e
e ax dx =
a
Z bx
a
bx
a dx = for a > 0
b log a
Z
log x dx = x log x − x

Z
1 1 x
dx = arctan
2
x + a 2 a a
(
Z 1 a−x 2 2
1 log for x < a
dx = 2a a+x
2
2
x − a 2 1 log x−a for x > a 2
2a x+a
Z
1 x x
2
√ dx = arcsin = − arccos for x < a 2
2
a − x 2 |a| |a|
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