Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 15/Definite Integrals involving Logarithmic Functions

Definite Integrals involving Logarithmic Functions

 * $15.90$: Definite Integral from $0$ to $1$ of $x^m \paren {\ln x}^n$


 * $15.91$: Definite Integral from $0$ to $1$ of $\dfrac {\ln x} {1 + x}$


 * $15.92$: Definite Integral from $0$ to $1$ of $\dfrac {\ln x} {1 - x}$


 * $15.93$: Definite Integral from $0$ to $1$ of $\dfrac {\map \ln {1 + x} } x$


 * $15.94$: Definite Integral from $0$ to $1$ of $\dfrac {\map \ln {1 - x} } x$


 * $15.95$: Definite Integral from $0$ to $1$ of $\ln x \map \ln {1 + x}$


 * $15.96$: Definite Integral from $0$ to $1$ of $\ln x \map \ln {1 - x}$


 * $15.97$: Definite Integral to Infinity of $\dfrac {x^{p - 1} \ln x} {1 + x}$


 * $15.98$: Definite Integral from $0$ to $1$ of $\dfrac {x^m - x^n} {\ln x}$


 * $15.99$: Definite Integral to Infinity of $e^{-x} \ln x$


 * $15.100$: Definite Integral to Infinity of $e^{-x^2} \ln x$


 * $15.101$: Definite Integral to Infinity of $\map \ln {\dfrac {e^x + 1} {e^x - 1} }$


 * $15.102$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\map \ln {\sin x}$ and $\map \ln {\cos x}$
 * $15.102.1$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\map \ln {\sin x}$
 * $15.102.2$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\map \ln {\cos x}$


 * $15.103$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\paren {\map \ln {\sin x}}^2$ and $\paren {\map \ln {\cos x}}^2$
 * $15.103.1$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\paren {\map \ln {\sin x}}^2$
 * $15.103.2$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\paren {\map \ln {\cos x}}^2$


 * $15.104$: Definite Integral from $0$ to $\pi$ of $x \map \ln {\sin x}$


 * $15.105$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin x \map \ln {\sin x}$


 * $15.106$: Definite Integral from $0$ to $2 \pi$ of $\map \ln {a + b \sin x}$ and $\map \ln {a + b \cos x}$
 * $15.106.1$: Definite Integral from $0$ to $2 \pi$ of $\map \ln {a + b \sin x}$
 * $15.106.2$: Definite Integral from $0$ to $2 \pi$ of $\map \ln {a + b \cos x}$


 * $15.107$: Definite Integral from $0$ to $\pi$ of $\map \ln {a + b \cos x}$


 * $15.108$: Definite Integral from $0$ to $\pi$ of $\map \ln {a^2 - 2 a b \cos x + b^2}$


 * $15.109$: Definite Integral from $0$ to $\dfrac \pi 4$ of $\map \ln {1 + \tan x}$


 * $15.110$: Definite Integral from $0$ to $\pi$ of $\sec x \map \ln {\dfrac {1 + b \cos x} {1 + a \cos x} }$


 * $15.111$: Definite Integral from $0$ to $a$ of $\map \ln {2 \sin \dfrac x 2}$