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Mathematics
Mathematics
Problem
For
x
>
0
x > 0
x
>
0
, let
f
(
x
)
=
∫
1
x
log
t
1
+
t
d
t
f(x) = \int_{1}^{x} \frac{\log t}{1+t} dt
f
(
x
)
=
∫
1
x
1
+
t
l
o
g
t
d
t
. Find the function
f
(
x
)
+
f
(
1
x
)
f(x) + f\left(\frac{1}{x}\right)
f
(
x
)
+
f
(
x
1
)
and find the value of
f
(
e
)
+
f
(
1
e
)
f(e) + f\left(\frac{1}{e}\right)
f
(
e
)
+
f
(
e
1
)
. a. Find the function
f
(
x
)
+
f
(
1
x
)
f(x) + f\left(\frac{1}{x}\right)
f
(
x
)
+
f
(
x
1
)
. b. Find the value of
f
(
e
)
+
f
(
1
e
)
f(e) + f\left(\frac{1}{e}\right)
f
(
e
)
+
f
(
e
1
)
.
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