Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection
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820 Principles of Radiation Interaction in Matter and Detection
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Probability and Statistics for Detection Systems 821
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822 Principles of Radiation Interaction in Matter and Detection
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Probability and Statistics for Detection Systems 823
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824 Principles of Radiation Interaction in Matter and Detection
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Probability and Statistics for Detection Systems 825
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826 Principles of Radiation Interaction in Matter and Detection
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Probability and Statistics for Detection Systems 827
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828 Principles of Radiation Interaction in Matter and Detection
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Table of Integrals 829
B.2 Table of Integrals
In this Appendix, the most commonly used integrals for the purposes of this book are
listed. More detailed treatments can be found in specialized Mathematical Handbooks.
R
(ax + b)
r
dx =
1
a (r+1)
(ax + b)
r+1
+ C, r 6= -1
R
1
q
(
a
2
−x
2
)
dx = arcsin
x
a
+ C
R
1
q
(
a
2
+x
2
)
dx = arcsinh
x
a
+ C
R
p
(a
2
− x
2
) dx
=
x
2
p
(a
2
− x
2
) +
a
2
2
arcsin
x
a
+ C
R
p
(a
2
+ x
2
) dx
=
x
2
p
(a
2
+ x
2
) +
a
2
2
arcsinh
x
a
+ C
R
1
ax+b
dx =
1
a
ln |(ax + b)| + C
R
xe
x
dx = e
x
(x − 1) + C
R
e
ax
dx =
1
a
e
ax
+ C, a 6= 0
R
a
x
dx =
1
ln a
a
x
+ C
R
ln x dx = x (ln x − 1) + C, (x > 0)
R
x ln x dx =
1
2
x
2
¡
ln x −
1
2
¢
+ C, (x > 0)
R
1
x ln x
dx = ln | ln x| + C, (x > 0)
R
x
m
(ln x)
n
dx m , n integers, and 6= -1
= −
n
m+1
R
x
m
(ln x)
n−1
dx, and (x > 0)
R
sin x dx = − cos x + C
R
cos x dx = sin x + C
R
x sin x dx = sin x − x cos x + C
R
cos
2
x dx =
1
2
(sin x cos x + x) + C
R
x sin x
2
dx = −
1
2
cos x
2
+ C
R
1
1+sin ax
dx = −
1
a
tan
¡
ax
2
−
π
4
¢
+ C
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