# Natural logarithm of natural logarithm

Can you find the integral of $$\int { \ln { \left( \ln { x } \right) } dx }$$

Note by Fredirick Estrella
2 years, 6 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

In terms of elementary functions? No.

But you can include the logarithmic integral $$\displaystyle \text{li}(x) = \int_0^x \dfrac{dt}{\ln t}$$, to get $$\displaystyle \int \ln(\ln x) \, dx = x \ln(\ln x) - \text{li}(x) + C$$.

Your first step is to use the substitution $$y = \ln x$$.

- 2 years, 6 months ago

×