How do you integrate int ln(x)/x dx using integration by parts?

1 Answer
Topscooter
Dec 20, 2015

intln(x)/xdx = ln(x)^2/4

Explanation:

Integration by parts is a bad idea here, you will constantly have intln(x)/xdx somewhere. It is better to change the variable here because we know that the derivative of ln(x) is 1/x.

We say that u(x) = ln(x), it implies that du = 1/xdx. We now have to integrate intudu.

intudu = u^2/2 so intln(x)/xdx = ln(x)^2/2

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