Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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

1 Answer

Apr 1, 2015

$\frac{{(ln (x))}^{2}}{2} + C$ $(ln(x))^2/2+C$ (Also written $\frac{1}{2} {ln}^{2} (x) + c$ $1/2ln^2(x)+c$ ).

Explanation:

$\frac{ln (x)}{x} = ln (x) \cdot (\frac{1}{x})$ $ln(x)/x=ln(x)*(1/x)$ .

The derivative of $ln x$ $lnx$ is $\frac{1}{x}$ $1/x$ , so

$ln (x) \cdot (\frac{1}{x})$ $ln(x)*(1/x)$ 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 $u^2/2 +C$ .)

Related questions

See all questions in Integrals of Exponential Functions

Impact of this question

2175 views around the world

You can reuse this answer
Creative Commons License