Divergent Integrals

HYPERGENERA

Monomial Integrals

$\displaystyle \int_x^{\infty_+} t^r \, dt = \dfrac{(x-1)^{r+1} - x^{r+1}}{r+1}$

$\displaystyle \int_x^{\infty_+} t^n \, dt = \dfrac{(x-1)^{n+1} - x^{n+1}}{n+1}$

$\displaystyle \int_x^{\infty_+} t^\frac{1}{m} \, dt = \dfrac{m}{m+1} \, \left((x-1)^\frac{m+1}{m} - x^\frac{m+1}{m}\right)$

$\displaystyle \int_{x^m}^{\infty_+^m} t^\frac{1}{m} \, dt = \dfrac{m}{m+1} \, \left((x-1)^{m+1} - x^{m+1}\right)$

$\displaystyle \int_{x^m}^{\infty_+^m} \dfrac{t^\frac{1}{m}}{m} \, dt = \dfrac{(x-1)^{m+1} - x^{m+1}}{m+1}$

$\displaystyle \int_x^{\infty_+} t^\frac{n}{m} \, dt = \dfrac{m}{n+m} \, \left((x-1)^\frac{n+m}{m} - x^\frac{n+m}{m}\right)$

$\displaystyle \int_x^{\infty_+} \dfrac{t^n}{n} \, dt = \dfrac{(x-1)^{n+1} - x^{n+1}}{n(n+1)}$

$\displaystyle \int_x^{\infty_+} \dfrac{t^n}{n!} \, dt = \dfrac{(x-1)^{n+1} - x^{n+1}}{(n+1)!}$

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