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- January 1st 2013, 02:18 PMNervousSpot the mistake.

- January 1st 2013, 02:28 PMemakarovRe: Spot the mistake.
There is no mistake.

- January 1st 2013, 02:31 PMLordoftheFliesRe: Spot the mistake.
There is none. I assume you are surprised because the answer book or whatever says

Both answers only differ by a constant, which disappears once you make the integral definite:

- January 1st 2013, 08:25 PMibduttRe: Spot the mistake.
Both the answers are right, You could have made the substitution as

Just change the substitution and you would get the desired answer.

u = cos(ln(x))

Now du = (-sin(ln(x)))/x dx

Thus the integral becomes

-∫▒udu = -u^2/2+C = - 〖cos〗^2 (ln(x) )+C