Integrating Logarithmic Functions: Understanding the Integral of Logy

In summary, the conversation is about finding the integral of logy, where the original function is \int\int -xlogy dy dx. The individual is confused about the integral of logy, as the book states it is ylogy-y but the derivative of logy is 1/ylna, where a is the base. However, after realizing that some calculus books use log(y) to represent the natural logarithm, the individual understands the solution.
  • #1
atwong713
20
0

Homework Statement



[tex]\int[/tex][tex]\int-xlogy dy dx[/tex]

the only problem i have is finding the integral of logy
i know i have to integrate my parts with u = logy and dv=dy
the book says the the integral of logy is ylogy-y but isn't the derivative of logy equal to 1/ylna where a is the base?
so isn't the integral of logy equal to ylogy-y/ln10 because of the base 10?
can someone clarify this for me?
 
Physics news on Phys.org
  • #2
I know some calculus books (especially the older ones I have looked at) use log(y) to designate the natural logarithm. Are you certain this isn't the case?
 
  • #3
oooo it is thanks makes a lot more sense now
 

What is the integral of log?

The integral of log is the inverse of the derivative of log. It is represented as ∫ln(x)dx and can be solved using integration techniques such as integration by parts or substitution.

How do I solve an integral of log?

To solve an integral of log, you can use integration techniques such as integration by parts or substitution. It is also important to remember the rules of integration and apply them accordingly.

Is there a specific formula for the integral of log?

Yes, there is a specific formula for the integral of log, which is ∫ln(x)dx. However, this formula can be modified and used in different forms depending on the integration technique being used.

What are some tips for solving an integral of log?

Some tips for solving an integral of log include carefully applying the rules of integration, using appropriate substitution techniques, and being familiar with the properties of log functions.

Can I use a calculator to solve an integral of log?

Yes, you can use a calculator to solve an integral of log. However, it is important to understand the steps and techniques involved in solving the integral by hand in order to accurately check the results from the calculator.

Similar threads

  • Calculus and Beyond Homework Help
Replies
20
Views
459
  • Calculus and Beyond Homework Help
Replies
1
Views
492
  • Calculus and Beyond Homework Help
Replies
4
Views
845
  • Calculus and Beyond Homework Help
Replies
3
Views
273
  • Calculus and Beyond Homework Help
Replies
7
Views
706
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
774
  • Calculus and Beyond Homework Help
Replies
4
Views
921
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
Back
Top