How do you find the antiderivative of $(cosx)/(x)$ ?

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Answer 1 · 2016-06-28T03:50:44

$ln x-(1/2)sum(-1)^nx^(2n)/(n(2n)!)+C, n=1, 2, 3,...,$

$and 0 < x<=1$ .

$cos x/x = sum((-1)^nx^(2n-1))/(2n)!, n=0, 1, 2, 3, ..,$ .for non-zero x.

$int cos x /x dx= int$ $sum((-1)^nx^(2n-1))/(2n)!, n=0, 1, 2, 3, ..,$ and# 0

< x<=1#.

$=ln x-(1/2)sum(-1)^nx^(2n)/(n(2n)!)+C, n=1, 2, 3,...,$

$and 0 < x<=1$ .

How do you find the antiderivative of (cosx)/(x) (cosx)/(x) ?