Table of Integrals, Series, and Products, 8th Edition

4.2–4.4 Logarithmic Functions

4.21 Logarithmic functions

4.211

1. 

${\displaystyle {\int }_e^{\infty }\frac{\text{d}x}{ln\frac{1}{x}}=-\infty }$

  BI (33)(9)

2. 

${\displaystyle {\int }_e^u\frac{\text{d}x}{lnx}=\text{li}\text{?}u}$

  FI III 653, FI II 606

4.212

1. 

$\begin{array}{ll}{\displaystyle {\int }_0^1\frac{\text{d}x}{a+lnx}}=e^{-a}\text{Ei}\left(a\right)\hfill & \left[a>0\right]\hfill \end{array}$

  BI (31)(4)

2. 

$\begin{array}{ll}{\displaystyle {\int }_0^1\frac{\text{d}x}{a-lnx}}=-e^a\text{Ei}\left(-a\right)\hfill & \left[a>0\right]\hfill \end{array}$

  BI (31)(5)

3.⁷ 

$\begin{array}{ll}{\displaystyle {\int }_0^1\frac{\text{d}x}{{\left(a+lnx\right)}^2}}=-\frac{1}{a}+e^{-a}\text{Ei}(a)\hfill & \left[a\ge 0\right]\hfill \end{array}$

  BI (31)(14)

4. 

$\begin{array}{ll}{\displaystyle {\int }_0^1\frac{\text{d}x}{{\left(a-lnx\right)}^2}}=\frac{1}{a}+e^a\text{Ei}\left(-a\right)\hfill & \left[a>0\right]\hfill \end{array}$

  BI (31)(16)

5.⁸ 

$\begin{array}{l}{\displaystyle {\int }_0^1\frac{lnx\text{d}x}{}}\hfill \end{array}$