need help in another integral

[vast knot]

$\int_{1}^{\infty}\frac{\ln(x)}{x\sqrt{x^2-1}}dx $

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[vast knot]

$\int_{1}^{\infty}\frac{\ln(x)}{x\sqrt{x^2-1}}dx$

[night shale]

myswordslaysfrrrr

[chrome talon]

Are these competitive integrals?

Anyways, trig-sub, and then queen's rule meaning let u=pi/2 - x.

[visual furnace]

Can’t you use Feynman’s technique then integrate ?

[visual furnace]

Like if you let I(t)= ∫ln(xt)/(xsqrt(t^2-1)) dx

You can evaluate I’(t) by using the substitution x=cosh(u)

I’m not sure if it works but you could try

But idk

@vast knot

[wind spoke]

$\int^{\infty}_{1}\frac{\ln{(x)}}{x\sqrt{x^2-1}}dx$

$\int^{\infty}_{0}\frac{1}{\sqrt{e^{2u}-1}}du$

$\int^{\infty}_{0}\frac{1}{2(v+1)\sqrt{v}}dv$

idk...

[night shale]

No Lifer (no lifer)

[night shale]

myswordslaysfrrrr

[vast knot]

AoPS

[chrome talon]

Gotcha