×

Tough Integral

This integral has always eluded me:

$\large \int e^{x} \ln(x) \, dx$

Does anyone know the general solution to it?

Note by Geoff Pilling
1 year, 10 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:

well,this can't be done until you introduce something called the exponential integral,you can read about it here,which doesn't have a closed form most of the time

the solution to the integral above is $e^x\ln(x)-\text{Ei}(x)$

where $$\text{Ei}$$ denotes the exponential integral

- 1 year, 10 months ago

Ah, cool, thanks Hummus! I'll take a look at it when I get a chance!

- 1 year, 10 months ago

just use the expansion for ln x and integrate and have an approx result.

- 1 year, 10 months ago