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

1 Answer

A. S. Adikesavan

Jun 28, 2016

#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 #.

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