Definite integrals 629
Z
dx
abxx
xb
+− ba
=
−
−2122
4
sin
=++++
lnx
b
abxx
2
2Z
dx
abxx++
2Zcot cot ln( )
−−=++
11 21
2
xdx x x 1 x
wherepx
b
a
q
bac
a
=+ , =
−
2
4
4
222=
−
<
−1
2
4
1
4
212aq
pq
pq
bac
aq
p
q
b
ln
tan
if
if aac
Z
dx
ax bx c
2++
Definite integrals
(n 1 ≠ 1 0, ninteger)
(m 1 ≠ 1 n, mand nintegers)
(m 1 ≠ 1 n, mand nintegers)
(all mand nintegers)
Z
00
πsin cosmx nx dx=
Z
00
πcos cosmx nx dx=
Z
00
πsin sinmx nx dx=
ZZ
02022
πππ
sin nx dx==cos nx dx
Z
0222
adx
ax−
=
π
Z
021122
∞xedx
n
a
naxn+−+=
!
Z
0212
13 2 12
∞xe dx
n
a
a
naxnn−+=
·-()− π
Z
02
12
∞edx
a
−ax=
π
Z
01∞xe dx
n
a
naxn−+=
!
Z
022∞ebxdx
a
ab
−ax=
cos
Z
022∞ebxdx
b
ab
−ax=
sin
Z
0∞cos cos
ln
ax bx
x
dx
b
a
−
=
Z
02
0
∞sin
()
ax
x
dx=, >a
π
Z
022 21
4
aaxdx a−=π