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Question Number 9482 by sou1618 last updated on 10/Dec/16

find  F_n (−1) or F_n (x).  n=1,2,3......  F_n (x)=∫(1+x^3 )^n dx

$${find}\:\:{F}_{{n}} \left(−\mathrm{1}\right)\:{or}\:{F}_{{n}} \left({x}\right). \\ $$$${n}=\mathrm{1},\mathrm{2},\mathrm{3}...... \\ $$$${F}_{{n}} \left({x}\right)=\int\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{{n}} {dx} \\ $$

Commented by sou1618 last updated on 10/Dec/16

it may be related to#9474.  F_n (x)=Σ_(k=0) ^n (1/(3k+1))x^(3k+1)  _n C_k =???  F_n (−1)=−Σ_(k=0) ^n (1/(3k+1))(−1)^k  _n C_k =???

$${it}\:{may}\:{be}\:{related}\:{to}#\mathrm{9474}. \\ $$$${F}_{{n}} \left({x}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}{x}^{\mathrm{3}{k}+\mathrm{1}} \:_{{n}} {C}_{{k}} =??? \\ $$$${F}_{{n}} \left(−\mathrm{1}\right)=−\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\left(−\mathrm{1}\right)^{{k}} \:_{{n}} {C}_{{k}} =??? \\ $$

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