♔Renascence_5

摘要： $$\Large\displaystyle \int_0^{1} \frac{\arccos^4 \left(x^2\right)}{\sqrt{1 x^2}}\,\mathrm{d}x$$ $\Large\mathbf{Solution:}$ Let $I$ denote the integral 阅读全文

摘要： $$\Large\displaystyle \int_0^1 \dfrac{\operatorname{Li}_2\left(\dfrac{x}{4}\right)}{4 x}\ln\left(\dfrac{1+\sqrt{1 x}}{1 \sqrt{1 x}}\right)\mathrm{d}x= 阅读全文

摘要： $$\Large\displaystyle \int_{0}^{1}\left \{ \frac{1}{x} \right \}\mathrm{d}x~，~\int_{0}^{1}\left \{ \frac{1}{x} \right \}^{2}\mathrm{d}x~，~\int_{0}^{1} 阅读全文

摘要： $$\Large\displaystyle \int_0^1\frac{\ln^3(1+x)\,\ln^3x}x\mathrm{d}x$$ $\Large\mathbf{Solution:}$ Using the following known results: $$\begin{align } \ 阅读全文