Products of Trigonometric Functions and Ex-
ponentials
(117)
Z
e
x
sin x dx =
1
2
e
x
(sin x - cos x)
(118)
Z
e
bx
sin ax dx =
1
a
2
+ b
2
e
bx
(b sin ax - a cos ax)
(119)
Z
e
x
cos x dx =
1
2
e
x
(sin x + cos x)
(120)
Z
e
bx
cos ax dx =
1
a
2
+ b
2
e
bx
(a sin ax + b cos ax)
(121)
Z
xe
x
sin x dx =
1
2
e
x
(cos x - x cos x + x sin x)
(122)
Z
xe
x
cos x dx =
1
2
e
x
(x cos x - sin x + x sin x)
Integrals of Hyperbolic Functions
(123)
Z
cosh ax dx =
1
a
sinh ax
(124)
Z
e
ax
cosh bx dx =
e
ax
a
2
- b
2
[a cosh bx - b sinh bx] a 6= b
e
2ax
4a
+
x
2
a = b
(125)
Z
sinh ax dx =
1
a
cosh ax
13
