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Mathematics
Mathematics
Problem
Which of the following is an antiderivative of
e
2
x
sin
2
x
e^{2x}\sin 2x
e
2
x
sin
2
x
? a)
e
2
x
4
(
cos
2
x
−
sin
2
x
)
+
C
\dfrac{e^{2x}}{4}\bigl(\cos 2x-\sin 2x\bigr)+C
4
e
2
x
(
cos
2
x
−
sin
2
x
)
+
C
b)
e
2
x
4
(
sin
2
x
+
cos
2
x
)
+
C
\dfrac{e^{2x}}{4}\bigl(\sin 2x+\cos 2x\bigr)+C
4
e
2
x
(
sin
2
x
+
cos
2
x
)
+
C
c)
e
2
x
4
(
sin
2
x
−
cos
2
x
)
+
C
\dfrac{e^{2x}}{4}\bigl(\sin 2x-\cos 2x\bigr)+C
4
e
2
x
(
sin
2
x
−
cos
2
x
)
+
C
d)
e
2
x
2
(
sin
2
x
−
cos
2
x
)
+
C
\dfrac{e^{2x}}{2}\bigl(\sin 2x-\cos 2x\bigr)+C
2
e
2
x
(
sin
2
x
−
cos
2
x
)
+
C
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