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Mathematics
Problem
Evaluate the indefinite integral
∫
x
e
2
x
d
x
\displaystyle \int x e^{2x}\,dx
∫
x
e
2
x
d
x
. a)
e
2
x
x
2
+
C
\dfrac{e^{2x}x}{2}+C
2
e
2
x
x
+
C
b)
e
2
x
(
x
2
+
1
4
)
+
C
e^{2x}\left(\dfrac{x}{2}+\dfrac14\right)+C
e
2
x
(
2
x
+
4
1
)
+
C
c)
e
2
x
(
x
2
−
1
4
)
+
C
e^{2x}\left(\dfrac{x}{2}-\dfrac14\right)+C
e
2
x
(
2
x
−
4
1
)
+
C
d)
e
2
x
(
x
−
1
2
)
+
C
e^{2x}\left(x-\dfrac12\right)+C
e
2
x
(
x
−
2
1
)
+
C
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