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Mathematics
Problem
Answer the following integrals. a. (i) Evaluate
∫
x
e
x
d
x
\displaystyle\int x e^{x}\,dx
∫
x
e
x
d
x
. b. (ii) Hence, determine
∫
(
x
e
x
+
e
x
)
d
x
\displaystyle\int \bigl(x e^{x}+e^{x}\bigr)\,dx
∫
(
x
e
x
+
e
x
)
d
x
, writing your final answer in factorised form.
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