... ♣advanced calculus♣... ⧫⧫ prove that: I=∫_1 ^( ∞) (((t^4 −6t^2 +1)ln(ln(t)))/((1+t^2 )^3 ))dt=((2G)/π) G : catalan constant...


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Question Number 125462 by mnjuly1970 last updated on 11/Dec/20

$. . . ♣ a d v a n c e d c a l c u l u s ♣ . . .$ $⧫ ⧫ p r o v e t h a t :$ $I = \int_{1}^{\infty} \frac{(t^{4} - 6 t^{2} + 1) l n (l n (t))}{{(1 + t^{2})}^{3}} d t = \frac{2 G}{π}$ $G : c a t a l a n c o n s t a n t . . .$
	Answered by mindispower last updated on 13/Dec/20

	$h e l l l o s i r s u r f o r t h i s r e s u l t ?$
	Commented by mnjuly1970 last updated on 16/Dec/20

	$s o u r c e : w i k i p e d i a . . . c a t a l a n$ $c o n s t a n t . . i n t e g r a l r e p r e s e n t a t i o n . . .$
	Commented by mindispower last updated on 16/Dec/20

	$h e l l o s i r o k i w i i l ? t r y i t$
	Commented by mnjuly1970 last updated on 16/Dec/20

	$s i n c e r l y y o u r s . . .$
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