What is the antiderivative of ln(x)/x?

1 Answer
Jim H
Apr 1, 2015

#(ln(x))^2/2+C# (Also written #1/2ln^2(x)+c#).

Explanation:

#ln(x)/x=ln(x)*(1/x)#.

The derivative of #lnx# is #1/x#, so

#ln(x)*(1/x)# is of the form: #f(x)*f'(x)#, so the antiderivative is #1/2 (f(x))^2 +C#.

(Alt notation: #ln(x)/x=ln(x)*(1/x)# is of the form #u (du)/(dx)# whose antiderivative is #u^2/2 +C#.)

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