Why, intuitively, does $log(x)$ come in as the integral of $1/x$, wheras the integral of other powers of $x$ are powers of $x$?
12217
What is so special about $\alpha=-1$ in the integral of $x^\alpha$?
59352
Computing: $\int_0^1 \sqrt[3]{x\log{\frac{1}x}} \, \mathrm dx$
102639
How to receive the result of the integral $ \int\frac{1}{x}dx$ is $\ln|x|$?
19716
What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
101045
Is there a closed form for the integral $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$?
25652
Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
146873
Why is $\log(e^z)\ne z$ in complex analysis?
15110
About irrational logarithms
152648
Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?
107119
A logarithmic integral $\int^1_0 \frac{\log\left(\frac{1+x}{1-x}\right)}{x\sqrt{1-x^2}}\,dx$
136185
How $a^{\log_b x} = x^{\log_b a}$?
63251
Evaluation of $\int^1_0\frac{x^b-x^a}{\ln x} d x=\ln{{\frac{1+b}{1+a}}}$
113394
What does O(log n) mean exactly?
2250
What is the $x$ in $\log_b x$ called?
24716
$\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.
127290
Intuition behind logarithm change of base
133614
Why is $x^{\log_x n}=n$?