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.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

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

See full answer below.


Learn more about this topic:

Loading...
How to Solve Integrals Using Substitution

from

Chapter 13 / Lesson 5
7.2K

Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.


Related to this Question

Explore our homework questions and answers library