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Mathematics
Mathematics
Problem
Find
∫
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)
3
2
1
+
x
3
+
C
\dfrac{3}{2}\sqrt{1+x^{3}}+C
2
3
1
+
x
3
+
C
b)
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
c)
2
3
1
+
x
3
+
C
\dfrac{2}{3}\sqrt{1+x^{3}}+C
3
2
1
+
x
3
+
C
d)
2
1
+
x
3
+
C
2\sqrt{1+x^{3}}+C
2
1
+
x
3
+
C
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