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Mathematics
Problem
Evaluate the expression
∫
x
(
x
2
+
5
)
4
cos
[
(
x
2
+
5
)
5
]
d
x
\displaystyle \int x\,(x^{2}+5)^{4}\,\cos\bigl[(x^{2}+5)^{5}\bigr]\,dx
∫
x
(
x
2
+
5
)
4
cos
[
(
x
2
+
5
)
5
]
d
x
. a. (i) Obtain the antiderivative in its simplest closed form. b. (ii) Confirm the correctness of your result by differentiating your answer and showing that it reproduces the given integrand.
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