r-1-0-pi-2-5-2-2-x-2r-dx-

Question Number 787 by 123456 last updated on 22/Mar/15

\underset{r = 1}{\sum^{+ \infty}} \sqrt{\underset{0}{\int^{π / 2}} 5 + Γ (\frac{2}{2 + x^{2 r}}) d x}

Commented by 123456 last updated on 13/Mar/15

\underset{r = 1}{\sum^{+ \infty}} \sqrt{\frac{5 π}{2} + \underset{0}{\int^{π / 2}} Γ (\frac{2}{2 + x^{2 r}}) d x}

Γ (z) = \underset{0}{\int^{+ \infty}} t^{z - 1} e^{- t} d t ℜ (z) > 0

0 < \frac{2}{2 + x^{2 r}} ⩽ 1, 0 ⩽ x ⩽ \frac{π}{2}

\frac{2^{2 r + 1}}{2^{2 r + 1} + π^{2 r}} ⩽ \frac{2}{2 + x^{2 r}} ≪ 1, 0 ⩽ x ⩽ \frac{π}{2}

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