♔Renascence_5

摘要： $$\Large\displaystyle \int_{0}^{1}x\sqrt{1+x^{3}}\mathrm{d}x$$ $\Large\mathbf{Solution:}$ 易知 $$\int_{0}^{1}x\sqrt{1+x^{3}}\mathrm{d}x=\frac{1}{3}\int_ 阅读全文

摘要： $$\Large\displaystyle \int_{0}^{[x]}\left ( t \left [ t \right ] \right )\mathrm{d}t=\frac{[x]}{2}$$ $\Large\mathbf{Proof:}$ 我们来看更一般的形式，令$m=\left \lfl 阅读全文

摘要： $$\Large\displaystyle \int_{0}^{1}\left [ \frac{1+\sqrt{1 x}}{x} +\frac{2}{\ln\left ( 1 x \right )}\right ]\mathrm{d}x$$ $\Large\mathbf{Solution:}$ 方法 阅读全文

摘要： Since the Clausen functions are intimately related to a number of other important special functions, such as Inverse Tangent Integrals, Polylogarithms 阅读全文