How does du replace the circled part of the question in this integral?

[november1992]

Homework Statement

http://img528.imageshack.us/img528/356/hwhelp.png

Homework Equations

http://img407.imageshack.us/img407/3696/uanddu.png

The Attempt at a Solution

This is the answer I got. I was wondering how du replaces the circled part of the question.

http://img546.imageshack.us/img546/8975/hwanswer.png

 

[november1992]

I just came up with this information now. Is it right?

http://img851.imageshack.us/img851/3763/uandupart2.png

 

[Mark44]

Homework Statement

http://img528.imageshack.us/img528/356/hwhelp.png

Homework Equations

http://img407.imageshack.us/img407/3696/uanddu.png

The Attempt at a Solution

This is the answer I got. I was wondering how du replaces the circled part of the question.

http://img546.imageshack.us/img546/8975/hwanswer.png

You have
$$du = \frac{e^{\sqrt{x}}}{2\sqrt{x}}dx = \frac{1}{2\sqrt{x}e^{-\sqrt{x}}}dx$$

The part you have circled (and including dx) is 2du.

 

[november1992]

Thanks, I get it now.