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2015 VTRMC
Problem 5
improper integral, arctan
improper integral, arctan
Source: VTRMC 2015 P5
May 5, 2021
calculus
integration
Problem Statement
Evaluate
∫
0
∞
arctan
(
π
x
)
−
arctan
(
x
)
x
d
x
\int^\infty_0\frac{\operatorname{arctan}(\pi x)-\operatorname{arctan}(x)}xdx
∫
0
∞
x
arctan
(
π
x
)
−
arctan
(
x
)
d
x
(where
0
≤
arctan
(
x
)
<
π
2
0\le\operatorname{arctan}(x)<\frac\pi2
0
≤
arctan
(
x
)
<
2
π
for
0
≤
x
<
∞
0\le x<\infty
0
≤
x
<
∞
).
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