Posted by Erika on Friday, May 24, 2013 at 9:55am.
find the indefinite integral of
(1/x)*(e^(2log[ 3,x])) dx
where 3 is base of the log
i cannot even figure out where to start :( please help. thank you

Indefinite Integrals  Steve, Friday, May 24, 2013 at 10:38am
log_3(x) = lnx/ln3
e^(2log_3(x))
= e^(2lnx/ln3)
= (e^(lnx))^(2/ln3)
= x^(2/ln3)
so you have
∫(1/x) x^(2/ln3) dx
= ∫x^(2/ln31) dx
= 1/(2/ln3) x^(2/ln3)
or
ln3/2 x^(2/ln3)

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