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[x+(1)/(x)=3],[x^(3)+(1)/(x^(8))=8]...

[x+(1)/(x)=3],[x^(3)+(1)/(x^(8))=8]

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int (x^(3))/(1+x^(8))dx=

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(x^(3))/(sqrt(1-x^(8)))

int (x^(3)dx)/(1+x^(8)) =

int(x^(3))/((1+x^(8)))dx

The co-efficient of x in the expansion of (1-2x^(3)+3x^(5))(1+(1)/(x))^(8) is:

If x-(1)/(x)=5,xne0 then what is the value of (x^(6)+3x^(3)-1)/(x^(6)-8x^(3)-1) ?