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Evaluate: \(\int_0^\infty(cot^{-1}x)^2dx\)

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in Definite Integral by (46.2k points)

Evaluate: \(\int_0^\infty(cot^{-1}x)^2dx\)

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 \(\int_0^\infty(cot^{-1}x)^2dx\)

Let I =  \(\int_0^\infty(cot^{-1}x)^2dx\)

and x = cot θ 

∴ dx = – cosec2 θ dθ

when x = 0, then θ = π/2

when x = ∞, then θ = 0

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