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(x+(1)/(x))^(6)...

`(x+(1)/(x))^(6)`

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`(x+(1)/(x))^(6)=.^(6)C_(0)x^(6)((1)/(x))^(0)+^(6)C_(1)x^(5)((1)/(x))^(1)+^(6)C_(2)x^(4)((1)/(x))^(2)+^(6)C_(3)x^(3)((1)/(x))^(3)+^(6)C_(4)x^(2)((1)/(x))^(4)+^(6)C_(5)x((1)/(x))^(5)+^(6)C_(6)x^(0)((1)/(x))^(6)`
`=.^(6)C_(0)*x^(6)+^(6)C_(1)*x^(4)+^(6)C_(2)*x^(2)+^(6)C_(3)*1+^(6)C_(4)*(1)/(x^(2))+^(6)C_(5)*(1)/(x^(4))+^(6)C_(6)*(1)/(x^(6))`
`=1*x^(6)+(6)/(1)*x^(4)+(6xx5)/(2xx1)x^(2)+(6xx5xx4)/(3xx2xx1)+(6xx5)/(2xx1)*(1)/(x^(2))+(6)/(1)*(1)/(x^(4))+1*(1)/(x^(6))`
`=x^(6)+6x^(4)+15x^(2)+20+(15)/(x^(2))+(6)/(x^(4))+(1)/(x^(6))`
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