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${\int }_{0}^{1}\left[\frac{{x}^{p-1}}{\left(p-q\right)\left(p-r\right)\left(p-s\right)}+\frac{{x}^{q-1}}{\left(q-p\right)\left(q-r\right)\left(q-s\right)}+\frac{{x}^{r-1}}{\left(r-p\right)\left(r-q\right)\left(r-s\right)}+\frac{{x}^{s-1}}{\left(s-p\right)\left(s-q\right)\left(s-r\right)}\right]\frac{\text{d}x}{{\left(ln\text{?}x\right)}^{2}}=\frac{1}{2}\left[\frac{{p}^{2}ln\text{?}p}{\left(p-q\right)\left(p-r\right)\left(p-s\right)}+\frac{{q}^{2}lnq}{\left(q-p\right)\left(q-r\right)\left(q-s\right)}+\frac{{r}^{2}ln\text{?}r}{\left(r-p\right)\left(r-q\right)\left(r-s\right)}+\frac{{s}^{2}\text{?}ln\text{?}s}{\left(s-p\right)\left(s-p\right)\left(s-r\right)}\right]$

BI (124)(16)

$[p>0,?q>0,?r>0,?s>0]$

4.269

1.

${\int }_{0}^{1}\sqrt{-ln\text{?}x}\frac{\text{d}x}{1+{x}^{2}}=\frac{\sqrt{\pi }}{2}\sum _{k=0}^{\infty }\frac{{\left(-1\right)}^{k}}{\sqrt{{\left(2k+1\right)}^{3}}}$

BI (115)(33)

2.11

${\int }_{0}^{1}\frac{\text{d}x}{\sqrt{-lnx\text{?}}\left(1+{x}^{2}\right)}=\sqrt{\pi }\sum _{k=0}^{\infty }\frac{{\left(-1\right)}^{k}}{\sqrt{2k+1}}$

BI (133)(2)

3.

$\begin{array}{l}{\int }_{0}^{1}\sqrt{\left(-}\hfill \end{array}$

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