628 AppendixStandard integrals
(a 1 ≠ 1 ±b)
(a 1 ≠ 1 ±b)
(a 1 ≠ 1 ±b)
Ztanhxdx=lncoshx
Zcoshxdx=sinhx
Zsinhxdx=coshx
Z
dx
x
x
12 −
=−
cos
cot
Z
dx
x
x
12 +
=
cos
tan
=−
−
−
1
2
cos(abx) cos( )
ab
abx
ab
Zsin cosax bx dx
=
−
−
1
2
sin(abx) sin( )
ab
abx
ab
Zcos cosax bx dx
=
−
−
−
1
2
sin(abx) sin( )
ab
abx
ab
Zsin sinax bx dx
Zcosec
2dx=−cotx
Zsec tan
2xdx= x
Zcot cot
2xdx=− x x−
Ztan tan ln( )
−−=−+
11 21
2
xdx x x 1 x
Zcos cos
−−=−−
112xdx x x 1 x
Zsin sin
−−=+−
112xdx x x 1 x
=
++
−ax
a
x
ax
212222
sinh
Z axdx
22Z
dx
ax
x
a
221=
−sinh
=−
+−
−ax
a
x
xa
212222
cosh
Z xadx
22−
Z
dx
xa
x
a
221−
=
−cosh
=
+−
−ax
a
x
ax
212222
sin
Z axdx
22−
Z
dx
ax
x
a
221−
=
−sin
Z
dx
ax
a
ax
ax
221
2
−=
−
ln
Z
dx
ax
a
x
a
2211
=
−tan