Integraciones

Question

<blockquote> <p>Integrar <span class="math-container">$$I(n)=\int_{-1}^\infty \frac{\ln^n(x+1)}{x^n}\mathrm dx$$</span></p> </blockquote> <p>Tengo <span class="math-container">$I(2)=\dfrac{2\pi^2}{3}$</span> y <span class="math-container">$I(3)=\pi^2$</span> pero no sé cómo hacerlo con <span class="math-container">$I(n)$</span>.</p>