Divergent Integrals

TRIBE

Laplace Transforms (r > 0 and s > 0)

\displaystyle \int_0^{\infty_+} t^{s-1} \, e^{rt} \, dt = -\dfrac{r}{s} \int_0^{\infty_+} t^s \, e^{rt} \, dt  = \dfrac{\Gamma(s)}{(-r)^s}

Exponential Integrals (r > 0 and s > 0)