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Closed form for $\int_0^\infty\arctan\Bigl(\frac{2\pi}{x-\ln\,x+\ln(\frac\pi2)}\Bigr)\frac{dx}{x+1}$ [closed]

How to find ${\large\int}_1^\infty\frac{1-x+\ln x}{x \left(1+x^2\right) \ln^2 x} \mathrm dx$? [closed]

On the Paris constant and $\sqrt[k]{1+\sqrt[k]{1+\sqrt[k]{1+\sqrt[k]{1+\dots}}}}$?

Integral $\int_0^1\frac{x^9\left(x^4+x^2-x-1-5\ln x\right)}{\left(x^{10}-1\right)\ln x}\mathrm dx$

Closed form for ${\large\int}_0^1\frac{\ln(1-x)\,\ln(1+x)\,\ln(1+2x)}{1+2x}dx$

What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

How to figure out the log of a number without a calculator?

Proof of the derivative of $\ln(x)$

Easy way to compute logarithms without a calculator?

Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$

Prove that $5/2 < e < 3$?

How to compute $\lim_{n\rightarrow\infty}\frac1n\left\{(2n+1)(2n+2)\cdots(2n+n)\right\}^{1/n}$

Does the logarithm function grow slower than any polynomial?

Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis

Find $\lim_{n\rightarrow\infty} \frac{\log(2 + 3^{n})}{2n}$

Solve the equation $2^x=1-x$

New posts in logarithms

Closed form for $\int_0^\infty\arctan\Bigl(\frac{2\pi}{x-\ln\,x+\ln(\frac\pi2)}\Bigr)\frac{dx}{x+1}$ [closed]

The logarithm is non-linear! Or isn't it?

Why must the base of a logarithm be a positive real number not equal to 1?

How should I be avoiding this mistake? (To avoid missing solutions)

Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$

How to find ${\large\int}_1^\infty\frac{1-x+\ln x}{x \left(1+x^2\right) \ln^2 x} \mathrm dx$? [closed]

On the Paris constant and $\sqrt[k]{1+\sqrt[k]{1+\sqrt[k]{1+\sqrt[k]{1+\dots}}}}$?

Integral $\int_0^1\frac{x^9\left(x^4+x^2-x-1-5\ln x\right)}{\left(x^{10}-1\right)\ln x}\mathrm dx$

Closed form for ${\large\int}_0^1\frac{\ln(1-x)\,\ln(1+x)\,\ln(1+2x)}{1+2x}dx$

What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

How to figure out the log of a number without a calculator?

Proof of the derivative of $\ln(x)$

Easy way to compute logarithms without a calculator?

Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$

Prove that $5/2 < e < 3$?

How to compute $\lim_{n\rightarrow\infty}\frac1n\left\{(2n+1)(2n+2)\cdots(2n+n)\right\}^{1/n}$

Does the logarithm function grow slower than any polynomial?

Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis

Find $\lim_{n\rightarrow\infty} \frac{\log(2 + 3^{n})}{2n}$

Solve the equation $2^x=1-x$