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Mathematics
Mathematics
Problem
Evaluate
∫
x
2
1
−
x
3
d
x
\displaystyle \int \frac{x^{2}}{\sqrt{\,1 - x^{3}\,}}\,dx
∫
1
−
x
3
x
2
d
x
. a)
−
1
3
1
−
x
3
+
C
-\dfrac{1}{3}\sqrt{1 - x^{3}} + C
−
3
1
1
−
x
3
+
C
b)
2
3
1
−
x
3
+
C
\dfrac{2}{3}\sqrt{1 - x^{3}} + C
3
2
1
−
x
3
+
C
c)
−
2
3
1
−
x
3
+
C
-\dfrac{2}{3}\sqrt{1 - x^{3}} + C
−
3
2
1
−
x
3
+
C
d)
−
2
3
(
1
−
x
3
)
3
/
2
+
C
-\dfrac{2}{3}(1 - x^{3})^{3/2} + C
−
3
2
(
1
−
x
3
)
3/2
+
C
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