find-U-n-0-1-1-x-2-1-x-4-1-x-2-n-dx-

Question Number 147101 by mathmax by abdo last updated on 18/Jul/21

find U_{n} = \int_{0}^{1} (1 + x^{2}) (1 + x^{4}) \dots . (1 + x^{2^{n}}) dx

Answered by gsk2684 last updated on 18/Jul/21

\underset{0}{\int^{1}} \frac{(1 - x^{2^{1}}) (1 + x^{2^{1}}) (1 + x^{2^{2}}) (1 + x^{2^{3}}) \dots (1 + x^{2^{n}})}{(1 - x^{2})} d x

\underset{0}{\int^{1}} \frac{(1 - x^{2^{2}}) (1 + x^{2^{2}}) (1 + x^{2^{3}}) \dots (1 + x^{2^{n}})}{(1 - x^{2})} d x

\underset{0}{\int^{1}} \frac{(1 - x^{2^{3}}) (1 + x^{2^{3}}) \dots (1 + x^{2^{n}})}{(1 - x^{2})} d x

\underset{0}{\int^{1}} \frac{(1 - x^{2^{4}}) \dots (1 + x^{2^{n}})}{(1 - x^{2})} d x

\underset{0}{\int^{1}} \frac{1 + x^{2^{n + 1}}}{1 - x^{2}} d x

\dots

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