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Question
Mathematics
The value of ∫ (d x/x √1-x3) is equal to
Q. The value of
∫
x
1
−
x
3
d
x
is equal to
522
156
Integrals
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A
3
1
ℓ
n
∣
∣
1
−
x
3
+
1
1
−
x
3
−
1
∣
∣
+
C
B
3
1
ℓ
n
∣
∣
1
−
x
2
−
1
1
−
x
2
+
1
∣
∣
+
C
C
3
1
ℓ
n
∣
∣
1
−
x
3
1
∣
∣
+
C
D
3
1
ℓ
n
∣
∣
1
−
x
3
∣
∣
+
C
Solution:
Put
1
−
x
3
=
t
2
⇒
−
3
x
2
d
x
=
2
t
d
t
I
=
∫
x
1
−
x
3
d
x
=
∫
x
3
1
−
x
3
x
2
d
x
=
−
3
1
∫
(
1
−
t
2
)
⋅
t
2
t
d
t
=
−
3
2
∫
1
−
t
2
d
t
=
3
2
∫
t
2
−
1
d
t
=
3.2
2.1
ℓ
n
∣
∣
1
+
t
1
−
t
∣
∣
=
3
1
ℓ
n
∣
∣
1
−
x
3
+
1
1
−
x
3
−
1
∣
∣
+
c