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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
2
x
(
x
2
+
1
)
2
e
(
x
2
+
1
)
3
f(x)=2x\,(x^{2}+1)^{2}\,e^{\,(x^{2}+1)^{3}}
f
(
x
)
=
2
x
(
x
2
+
1
)
2
e
(
x
2
+
1
)
3
. a. (i) Evaluate the indefinite integral
∫
f
(
x
)
d
x
\displaystyle \int f(x)\,dx
∫
f
(
x
)
d
x
. Express your answer in its simplest form. b. (ii) Using the result of part (i), calculate the exact value of
∫
0
1
f
(
x
)
d
x
\displaystyle \int_{0}^{1} f(x)\,dx
∫
0
1
f
(
x
)
d
x
. Simplify your final answer.
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