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Mathematics
Mathematics
Problem
Prove that
∫
0
1
tan
−
1
x
x
d
x
=
1
2
∫
0
π
2
x
sin
x
d
x
\int_{0}^{1} \frac{\tan^{-1} x}{x} dx = \frac{1}{2} \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin x} dx
∫
0
1
x
t
a
n
−
1
x
d
x
=
2
1
∫
0
2
π
s
i
n
x
x
d
x
.
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