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Question Number 131138 by liberty last updated on 02/Feb/21

∫_0 ^( 1)  ((arctan (√(x^2 +2)))/((x^2 +1)(√(x^2 +2)))) dx =?

$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{arctan}\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}}\:\mathrm{dx}\:=? \\ $$

Answered by EDWIN88 last updated on 02/Feb/21

=((5π^2 )/(96))

$$=\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{96}} \\ $$

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