∫∞
0
dx
1 −xn=
π
ncot
π
n
∫∞
0
dx
(a^2 x^2 +c^2 )(x^2 +b^2 )=
π
2 bc
1
c+ab
∫∞
0
dx
(a^2 +x^2 )(b^2 +x^2 )=
π
2
1
ab(a+b)
∫∞
0
dx
(a^2 −x^2 )(x^2 +p^2 )=
π
2 p
1
a^2 +p^2
∫∞
0
x^2 dx
(a^2 −x^2 )(x^2 +p^2 )=
π
2
p
a^2 +p^2
∫∞
0
x^2 dx
(x^2 +a^2 )(x^2 +b^2 )(x^2 +c^2 )=
π
2(a+b)(b+c)(c+a)
∫∞
0
√x dx
1 +x^2 =
√π
2
∫∞
0
x dx
(1 +x)(1 +x^2 )=
π
4
Integrals containing trigonometric terms
∫ 1
0
sin−^1 x
x dx=
π
2 ln 2
∫π/ 2
0
tan−^1 (abtanθ)dθ
tanθ =
π
2 ln|1 +
b
a|
∫π/ 2
0
sin^2 x dx=π 4
∫π/ 2
0
cos^2 x dx=π 4
∫π/ 2
0
dx
a+bcosx=
cos√−^1 (b/a)
a^2 −b^2
∫π/ 2
0
sin^2 m−^1 xcos^2 n−^1 x dx=B(m, n) =Γ(Γ(mm)Γ(+nn)), m > 0 , n > 0
∫π/ 2
0
sinpxcosqx dx=Γ(
p+1
2 )Γ(
q+1
2 )
2Γ(p+ 2 q+ 1)
∫π/ 2
0
dx
1 + tanmx=
π
4
∫π
0
cospθcosqθ dθ=
{ 0 , p 6 =q
π
2 , p=q
Appendix C
