Question:
Integration of Cosx/x
With Solution
Answer:
The expansion of cos x is
cos x = 1 - x2 /2! + x4 /4! - x6 /6! + ...
Dividing this by x, we get
cos x = 1/x - x/2! + x3 /4! - x5 /6! + ...
And finally, integrating this series term by term gives us a power series expansion for
the integral of cos x/x
∫ cos x/x dx = Log x - x2 /(2*2!) + x4 /(4*4!) - x6 /(6*6!) + ......... + C
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