The deep reason why $\int \frac{1}{x}\operatorname{d}x$ is a transcendental function ($\log$)
112551
Demystify integration of $\int \frac{1}{x} \mathrm dx$
82311
Computing the primitive $\int\frac{1}{1+x^n} dx$
828
Computing the integral of $\log(\sin x)$
69803
An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$
91306
Integration of $\frac{1}{\log(x)}$
65407
Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
102639
How to receive the result of the integral $ \int\frac{1}{x}dx$ is $\ln|x|$?
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
19716
What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
6571
A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$
22486
What does $\log^{2}{x}$ mean?
8289
Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$
119477
Understanding the Definition of $\int_\gamma f\ \overline{dz}$
88154
Proving $\int_{0}^1\frac{x-1}{\log x}dx=\log 2$ and $\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$
135653
An integral$\frac{1}{2\pi}\int_0^{2\pi}\log|\exp(i\theta)-a|\text{d}\theta=0$ which I can calculate but can't understand it.
66902
Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
42306
Motivation for Napier's Logarithms