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Mathematics
Problem
It is known that
∫
e
2
x
sin
(
3
x
)
d
x
=
e
2
x
(
2
sin
(
3
x
)
−
3
cos
(
3
x
)
)
13
+
C
\displaystyle\int e^{2x}\sin(3x)\,dx=\dfrac{e^{2x}\bigl(2\sin(3x)-3\cos(3x)\bigr)}{13}+C
∫
e
2
x
sin
(
3
x
)
d
x
=
13
e
2
x
(
2
sin
(
3
x
)
−
3
cos
(
3
x
)
)
+
C
. Using this information, determine
∫
e
2
x
cos
(
3
x
)
d
x
\displaystyle\int e^{2x}\cos(3x)\,dx
∫
e
2
x
cos
(
3
x
)
d
x
and include the constant of integration.
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