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Mathematics
Mathematics
Problem
Let
J
=
∫
0
1
12
x
2
(
1
+
x
3
)
3
e
(
1
+
x
3
)
4
d
x
J=\displaystyle \int_{0}^{1} 12x^{2}\,(1+x^{3})^{3}\,e^{\,(1+x^{3})^{4}}\,dx
J
=
∫
0
1
12
x
2
(
1
+
x
3
)
3
e
(
1
+
x
3
)
4
d
x
. a. (i) Evaluate
J
J
J
exactly, showing all necessary steps. b. (ii) Prove that your final answer simplifies to
e
16
−
e
e^{16}-e
e
16
−
e
.
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