# Find the indefinite integral by substitution: {eq}\displaystyle \int \frac {\ln(5x)}{x} \ dx {/eq}

## Question:

Find the indefinite integral by substitution: {eq}\displaystyle \int \frac {\ln(5x)}{x} \ dx {/eq}

## Solving Integrals Using Substitution:

To solve an indefinite integral, it is often necessary to perform some mathematical tricks to convert it into a common integral (standard) found in the integral table. The substitution method allows us to convert some integrals into a common integral, for this we must make a variable change that allows us to solve the integral directly using a standard integral already known. Once the change of variable or substitution has been made, the integral is resolved and the substitution is undone in order to present the solution in its original variable.

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{eq}\eqalign{ & {\text{Let's evaluate the following integral }}\int {\frac{{\ln \left( {5x} \right)}}{x}dx} {\text{:}} \cr & {\text{applying the...