Begin2.DVI

∫ 1

0

ln(1−x)

x dx=−

π^2

6

∫ 1

0

(ax^2 +bx+c)

ln^1 x

1 −xdx= (a+b+c)

π^2

6 −(a+b)−

a

4

∫ 1

0

√lnx^1

1 −x^2

dx=π 2 ln2

∫ 1

0

1 −xp−^1

(1−x)(1−xp)(ln

1

x)

2 n− (^1) dx=^1
4 n(1−
1
p^2 n)(2π)
2 nB 2 n− 1
96.
∫ 1
0
xm−xn
lnx dx= ln
∣∣
∣∣1 +m
1 +n
∣∣
∣∣
97.
∫ 1
0
xp(lnx)ndx=



(−1)n(p+ 1)n!n+1, n an integer
(−1)n(Γ(p+ 1)n+ 1)n+1, n noninteger
98.
∫π/ 4
0
ln(1 + tanx)dx=π 8 ln2
99.
∫π/ 2
0
ln sinθ dθ=π 2 ln(^12 )
100.
∫π
0
ln(a+bcosx)dx=πln
∣∣
∣∣
∣
a+
√
a^2 +b^2
2
∣∣
∣∣
∣
101.
∫ 2 π
0
ln(a+bcosx)dx= 2πln|a+
√
a^2 −b^2 |
102.
∫ 2 π
0
ln(a+bsinx)dx= 2iln|a+
√
a^2 −b^2 |
103.
∫∞
0
e−axdx=^1 a
104.
∫∞
0
xne−axdx=Γ(ann+1+ 1
105.
∫∞
0
e−a^2 x^2 dx= 21 a√π= 21 aΓ(^12 )
106.
∫∞
0
xne−a^2 x^2 dx=Γ(
m+1 2 )
2 am+1
107.
∫∞
0
e−axcosbx dx=a (^2) +ab 2
108.
∫∞
0
e−axsinbx dx=a (^2) +bb 2
Appendix C