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Mathematics
Problem
Determine the antiderivative of
∫
x
e
2
x
d
x
\displaystyle \int x e^{2x}\,dx
∫
x
e
2
x
d
x
. a)
1
2
x
e
2
x
−
1
4
e
2
x
+
C
\dfrac12 x e^{2x} - \dfrac14 e^{2x} + C
2
1
x
e
2
x
−
4
1
e
2
x
+
C
b)
1
2
x
e
2
x
+
1
4
e
2
x
+
C
\dfrac12 x e^{2x} + \dfrac14 e^{2x} + C
2
1
x
e
2
x
+
4
1
e
2
x
+
C
c)
x
e
2
x
−
1
2
e
2
x
+
C
x e^{2x} - \dfrac12 e^{2x} + C
x
e
2
x
−
2
1
e
2
x
+
C
d)
1
2
x
2
e
2
x
+
C
\dfrac12 x^{2} e^{2x} + C
2
1
x
2
e
2
x
+
C
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