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Mathematics
Problem
Consider the function
h
(
x
)
=
5
(
3
x
4
−
2
x
3
)
−
7
(
3
x
4
−
2
x
3
)
+
4
e
2
x
−
6
e
2
x
h(x)=5\bigl(3x^{4}-2x^{3}\bigr)-7\bigl(3x^{4}-2x^{3}\bigr)+4e^{2x}-6e^{2x}
h
(
x
)
=
5
(
3
x
4
−
2
x
3
)
−
7
(
3
x
4
−
2
x
3
)
+
4
e
2
x
−
6
e
2
x
. (i) Simplify
h
(
x
)
h(x)
h
(
x
)
before integrating. (ii) Find
∫
h
(
x
)
d
x
\displaystyle \int h(x)\,dx
∫
h
(
x
)
d
x
. (iii) Differentiate your answer to part (ii) and verify that it equals the simplified integrand obtained in part (i).
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