Question:
integrate cosx/x
Answer:
cosx = 1 - x2 /2! + x4 /4! - x6 /6! +...............
cosx/x = (1 - x2 /2! + x4 /4! - x6 /6! +...............)/x
=> cosx/x = 1/x - x /2! + x3 /4! - x5 /6! +...............
Now
∫cosx/x = ∫(1/x - x /2! + x3 /4! - x5 /6! +...............)
=> ∫cosx/x = log|x| - x2 /(2! *2) + x4 /(4*4!) - x6 /(6*6!)+............... + C {C is an integral constant}
=> ∫cosx/x = log|x| - x2 /4 + x4 /96 - x6 /4320 +............... + C
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