Answers and Explanations 503
Answers
801–900
834.
2
3
1
3
3 2
x
C
+
(
) +
The given integral is
3
1
2
3
x x
dx
+
∫
If you let u = x
3
+ 1, then du = 3x
2
dx. Substitute into the original integral and solve:
udu
u du
u
C
u
C
x
C
∫
∫
=
=
+
=
+
=
+
(
) +
1 2
3 2
3 2
3
3 2
3 2
2
3
2
3
1
835.
2 tan x C
( ) +
The given integral is
sec
sec
2
2
1
x
x
dx
x x
dx
∫
∫
=
If you let u
x x
=
=
1 2
, then you get du
x dx
x
dx
=
=
−
1
2
1
2
1 2
, or equivalently,
2
1
du
x
dx
=
. Substitute into the original integral:
2
2
2
2
sec
t an
tan
u du
u C
x C
( ) =
( )+
=
( ) +
∫
836.
−
+
+
6
35 4 5
7
(
)
x
C
Here’s the given integral:
6
4 5
8
+
(
)
∫
x
dx
If you let u = 4 + 5x, then you get du = 5
 
dx, or 1
5
du dx
= . Substitute into the original
integral:
6 1
5
6
5
6
5
7
6
35
6
35 4 5
8
8
7
7
7
u
du
u du
u
C
u
C
x
C
∫
∫
=
=
−





 +
= −
+
= −
+
(
)
+
−
−