We will use integration by substitution, as well as the integrals
∫
1
x
d
x
=
ln
|
x
|
+
C
and
∫
1
d
x
=
x
+
C
∫
x
3
x
2
+
1
d
x
=
∫
x
2
x
2
+
1
x
d
x
=
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
Let
u
=
x
2
+
1
⇒
d
u
=
2
x
d
x
. Then
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
=
1
2
∫
u
−
1
u
d
u
=
1
2
∫
(
1
−
1
u
)
d
u
=
1
2
(
u
−
ln
|
u
|
)
+
C
=
x
2
+
1
2
−
ln
(
x
2
+
1
)
2
+
C
=
x
2
2
−
ln
(
x
2
+
1
)
2
+
1
2
+
C
=
x
2
−
ln
(
x
2
+
1
)
2
+
C
Final answer
Answer:
5 more games to be won for the 50% success rate.
Step-by-step explanation:
Total number games played = 500
Number of successful games = 49% of 500
= 500 × 
= 245
Number of successful games for the success of 50% = 500 × 
= 250
Therefore, number of game you have to win more = 250 - 245
= 5 games
Answer:
180,000 m
Step-by-step explanation:
There are 60 seconds in a minute, so:
2 min × 60 s/min = 120 s
Distance = rate × time
d = 1500 m/s × 120 s
d = 180,000 m
Answer: b
Step-by-step explanation:
I took the test and got it right
good luck!