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Question Number 123639 by benjo_mathlover last updated on 26/Nov/20

   ∫_0 ^∞  (√(tan^(−1) (x))) dx ?

$$\:\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\sqrt{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}\:{dx}\:? \\ $$

Answered by MJS_new last updated on 27/Nov/20

x→+∞ ⇒ arctan x → (π/2) ⇒  integral doesn′t converge

$${x}\rightarrow+\infty\:\Rightarrow\:\mathrm{arctan}\:{x}\:\rightarrow\:\frac{\pi}{\mathrm{2}}\:\Rightarrow \\ $$$$\mathrm{integral}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{converge} \\ $$

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