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

Question

↳Redirected from "Find the limit as x approaches infinity of #xsin(1/x)#?"

3935 views around the world

You can reuse this answer
Creative Commons License

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 #.