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Question Number 56358 by harish 12@g last updated on 15/Mar/19

∫_0 ^∞ (cot^(−1) x)^2 dx

$$\int_{\mathrm{0}} ^{\infty} \left(\mathrm{cot}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} {dx} \\ $$$$ \\ $$

Commented by MJS last updated on 15/Mar/19

=πln 2

$$=\pi\mathrm{ln}\:\mathrm{2} \\ $$

Commented by harish 12@g last updated on 16/Mar/19

ful ans.

$${ful}\:{ans}. \\ $$

Commented by MJS last updated on 16/Mar/19

I approximated and then tried if my result  is something exact...  the integral cannot be solved elementarily

$$\mathrm{I}\:\mathrm{approximated}\:\mathrm{and}\:\mathrm{then}\:\mathrm{tried}\:\mathrm{if}\:\mathrm{my}\:\mathrm{result} \\ $$$$\mathrm{is}\:\mathrm{something}\:\mathrm{exact}... \\ $$$$\mathrm{the}\:\mathrm{integral}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{elementarily} \\ $$

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