# How do you use substitution to integrate #(ln(5x)/x)*dx#?

The integral is evaluated below.

We have to evaluate the integral,

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To integrate the expression (\frac{{\ln(5x)}}{x} , dx) using substitution, let (u = \ln(5x)). Then (du = \frac{1}{x} dx).

Rewrite the integral in terms of (u): [ \int \frac{u}{5} , du ]

Now integrate with respect to (u): [ \frac{1}{10} u^2 + C ]

Substitute back for (u): [ \frac{1}{10} (\ln(5x))^2 + C ]

So, the integral of (\frac{{\ln(5x)}}{x} , dx) is (\frac{1}{10} (\ln(5x))^2 + C), where (C) is the constant of integration.

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