# Check my Integration Homework: 1/x dx = (1/3)ln(ln(x)) + c

• Qube
In summary, the conversation discussed a solution to the integral of 1/x, which is ln(x). The solution was compared to the answer provided in a book, which was (1/3)ln(ln(x)) + c. It was noted that both answers are correct, with the difference being an extra additive constant. It was also suggested to use the property ln(x^3) = 3ln(x) to show that the two answers are equivalent.
Qube
Gold Member

## Homework Statement

http://i.minus.com/j5qAhbyrxc1jX.jpg

∫1/x dx = ln(x)

## The Attempt at a Solution

Can you guys check my work? I got the solution above and I've been pounding my head against the wall for the last two hours as to why that solution, according to my book, is incorrect.

The solution, according to the book, is

(1/3)ln(ln(x)) + c

Last edited by a moderator:
If you use that ln(x^3)=3*ln(x) you can show that your answer is the same as the books, with an extra additive constant.

Both answers are correct. If you differentiate both answers, you wind up with the integrand.

Tip: Your work would have been simpler if you had written ln(x3) as 3ln(x).

## What is the integration rule used to solve this problem?

The integration rule used to solve this problem is the inverse function rule.

## How do you check if the integration is correct?

To check if the integration is correct, you can take the derivative of the integrated function and see if it matches the original function.

## Why is there a constant (c) at the end of the integrated function?

The constant (c) represents the constant of integration, which is added to account for any possible missing terms in the original function.

## What is the significance of the natural logarithm (ln) in the integrated function?

The natural logarithm (ln) is used because it is the inverse of the exponential function, which is the derivative of the natural logarithm.

## Are there any restrictions on the value of x in this integration?

Yes, the value of x should be greater than 0 in order for the integration to be valid.

Replies
54
Views
9K
Replies
3
Views
1K
Replies
3
Views
6K
Replies
4
Views
1K
Replies
5
Views
2K
Replies
8
Views
1K
Replies
12
Views
2K
Replies
6
Views
1K
Replies
8
Views
972
Replies
1
Views
1K