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Mathematics
Mathematics
Problem
If an antiderivative of
f
(
x
)
f(x)
f
(
x
)
is
e
x
e^x
e
x
and that of
g
(
x
)
g(x)
g
(
x
)
is
cos
x
\cos x
cos
x
, then
∫
f
(
x
)
cos
x
d
x
+
∫
g
(
x
)
e
x
d
x
=
\int f(x)\cos x\,dx + \int g(x)e^x\,dx =
∫
f
(
x
)
cos
x
d
x
+
∫
g
(
x
)
e
x
d
x
=
(a)
f
(
x
)
g
(
x
)
+
c
f(x)g(x) + c
f
(
x
)
g
(
x
)
+
c
(b)
f
(
x
)
+
g
(
x
)
+
c
f(x) + g(x) + c
f
(
x
)
+
g
(
x
)
+
c
(c)
e
x
cos
x
+
c
e^x\cos x + c
e
x
cos
x
+
c
(d)
f
(
x
)
−
g
(
x
)
+
c
f(x) - g(x) + c
f
(
x
)
−
g
(
x
)
+
c
(a)
f
(
x
)
g
(
x
)
+
c
f(x)g(x) + c
f
(
x
)
g
(
x
)
+
c
(b)
f
(
x
)
+
g
(
x
)
+
c
f(x) + g(x) + c
f
(
x
)
+
g
(
x
)
+
c
(c)
e
x
cos
x
+
c
e^x\cos x + c
e
x
cos
x
+
c
(d)
f
(
x
)
−
g
(
x
)
+
c
f(x) - g(x) + c
f
(
x
)
−
g
(
x
)
+
c
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