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Mathematics
Problem
Let
k
≠
0
k\neq 0
k
=
0
be a constant. Determine
∫
x
e
k
x
d
x
\displaystyle \int x e^{k x}\,dx
∫
x
e
k
x
d
x
in terms of
k
k
k
. a)
x
e
k
x
k
+
e
k
x
k
2
+
C
\dfrac{x e^{k x}}{k} + \dfrac{e^{k x}}{k^{2}} + C
k
x
e
k
x
+
k
2
e
k
x
+
C
b)
x
e
k
x
k
−
e
k
x
k
+
C
\dfrac{x e^{k x}}{k} - \dfrac{e^{k x}}{k} + C
k
x
e
k
x
−
k
e
k
x
+
C
c)
x
e
k
x
k
−
e
k
x
k
2
+
C
\dfrac{x e^{k x}}{k} - \dfrac{e^{k x}}{k^{2}} + C
k
x
e
k
x
−
k
2
e
k
x
+
C
d)
x
e
k
x
k
+
C
\dfrac{x e^{k x}}{k} + C
k
x
e
k
x
+
C
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