- Evaluate the indicated integrals.
(1)
e x x dx x
(3 + 2sin + cos )
(2)
dx
x x
x
- )
2 3
(
5
(3)
dx
x x
x x
+
2 2
2 2
sin
sin
(4)
dx
x x
x
2 2
sin cos
cos 2
(5)
x x dx
+
2 5
( 1)
(6)
dx
e
e
x
x
2 +
(7)
dx
x
x
−
4
1
2
(8)
e dx x
+
2
( 1)
(9)
- 2 + 3
2
x x
dx
(10)
dx
x
x
+
sin 2
1 cos 2
2
(11)
dt
e
e
t
t
−
6
3
4
(12)
x (1+ x)
dx
(13)
+
dx
x x
x
(1 )
arctan
(14)
x xdx 3 2
sin cos
(15)
xdx 3
tan
(16)
- −
2
1 1 x
dx
(17)
−
−
dx
x
x
2
9 4
1
(18)
dx
a x
x
−
2 2
2
(19)
+
2 3
(x 1)
dx
(20)
3t + 4
tdt
(21)
+
dx
x x
x
2
( ln )
1 ln
(22)
−
2
4x x
dx
(23)
− +
−
dx
x x
x
6 18
2 1
2
(24)
1 1
1
x
x
x e dx
x
−
+ +
- Evaluate the indicated integrals.
(1)
xe dx x
−2
(2)
dx
x
x
2
ln
(3)
x dx
ln(1+ )
2
(4)
x x dx
arctan 2
(5)
−
e xdx x
sin 2 - If an antiderivative of
f (x)
is
(1 sin ln + x x ) ，find
( )
xf
x dx. - Evaluate the indicated integrals.
(1)
dx
x x
x
− −
+
( 1)( 2)
1
(2)
(
)
(
)
2
1 1
dx
x x + +
(3)
dx
x
x
x
x
+
−
−
−
6
2 20 22