Divergent Integrals

SUBGENERA

Monomial Integrals

$\displaystyle \int_1^{\infty_+} t^r \, dt = -\dfrac{1}{r+1}$

$\displaystyle \int_1^{\infty_+} t^n \, dt = -\dfrac{1}{n+1}$

$\displaystyle \int_1^{\infty_+} t^{2n-1} \, dt = -\dfrac{1}{2n}$

$\displaystyle \int_1^{\infty_+} t^{2n} \, dt = -\dfrac{1}{2n+1}$

$\displaystyle \int_1^{\infty_+} t^{2n+1} \, dt = -\dfrac{1}{2(n+1)}$

Polynomial Ratio Integrals

$\displaystyle \int_1^{\infty_+} \dfrac{t^n}{1+t} \, dt = (-1)^n \, (H_n' - \ln2) = \dfrac{1}{2} \, (H_{\frac{n-1}{2}} - H_{\frac{n}{2}})$

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