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Mathematics
Mathematics
Problem
For
x
>
0
x>0
x
>
0
, let
P
(
x
)
=
∫
4
ln
x
1
1
+
t
2
d
t
P(x)=\displaystyle\int_{4}^{\ln x} \frac{1}{1+t^{2}}\,dt
P
(
x
)
=
∫
4
l
n
x
1
+
t
2
1
d
t
. Determine
P
′
(
x
)
P'(x)
P
′
(
x
)
. a)
1
1
+
(
ln
x
)
2
\dfrac{1}{1+(\ln x)^{2}}
1
+
(
ln
x
)
2
1
b)
ln
x
1
+
(
ln
x
)
2
\dfrac{\ln x}{1+(\ln x)^{2}}
1
+
(
ln
x
)
2
ln
x
c)
1
x
(
1
+
(
ln
x
)
2
)
\dfrac{1}{x\bigl(1+(\ln x)^{2}\bigr)}
x
(
1
+
(
ln
x
)
2
)
1
d)
1
1
+
x
2
\dfrac{1}{1+x^{2}}
1
+
x
2
1
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