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2018 VTRMC
1
2018 VTRMC #1
2018 VTRMC #1
Source: VTRMC 2018
December 3, 2018
calculus
Problem Statement
It is known that
∫
1
2
x
−
1
arctan
(
1
+
x
)
d
x
=
q
π
ln
(
2
)
\int_1^2x^{-1}\arctan (1+x)\ dx = q\pi\ln(2)
∫
1
2
x
−
1
arctan
(
1
+
x
)
d
x
=
q
π
ln
(
2
)
for some rational number
q
.
q.
q
.
Determine
q
.
q.
q
.
Here,
0
≤
arctan
(
x
)
<
π
2
0\leq\arctan(x)<\frac{\pi}{2}
0
≤
arctan
(
x
)
<
2
π
for
0
≤
x
<
∞
.
0\leq x <\infty.
0
≤
x
<
∞.
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