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Find the term independent of x in the ex...

Find the term independent of x in the expansion of `(2^(x) + 2^(-x)+log_(e)e^(x+2)))^(30)`.

Text Solution

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We have `(2^(x) + 2^(-x)+log_(e)e^(x+2))^(30)`
`= (2^(x)+2^(-x)+x+2)^(30)`
` = ((2x^(x//2) + 2^(-x//2))^(2) + x )^(30)`
Therefore, the term independent of x occurs in `.^(30)C_(0)(2^(x//2) + 2^(-x//2))^(60)` which is `.^(30)C_(0) xx .^(60)C_(30)` or `.^(60)C_(30)`.
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