Question

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

Answer 1

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

`and 0 < x<=1`.

Explanation:

`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`.