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Mathematics
Problem
Compute
∫
0
1
x
3
(
x
4
+
1
)
5
/
2
d
x
\displaystyle \int_{0}^{1} x^{3}\,(x^{4}+1)^{5/2}\,dx
∫
0
1
x
3
(
x
4
+
1
)
5/2
d
x
. Which of the following is the exact value of the integral? a)
8
2
+
1
14
\dfrac{8\sqrt{2}+1}{14}
14
8
2
+
1
b)
8
2
−
1
14
\dfrac{8\sqrt{2}-1}{14}
14
8
2
−
1
c)
8
2
−
1
7
\dfrac{8\sqrt{2}-1}{7}
7
8
2
−
1
d)
8
2
−
1
28
\dfrac{8\sqrt{2}-1}{28}
28
8
2
−
1
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