1. ## Integrat with substitution

I need to find the Integral with respect to x of (e^(-.02x))/(8-e^(-.02x))

I use u=8-e^(-.02x)

and find that dx= du/.02e^(-.02x) or dx=50du/e^(-.02x)

when i substitute that back into the integral, the integral reduces to:

integral of (50/u)du which equals 50ln(abs(u))+ c

after substituting back in for u I finished with

50ln(abs(8-e^(-.02x)))

Where did I mess up?

2. ## Re: Integrat with substitution

$\displaystyle 50\ln\left(|8-e^{-.02x}|\right) + C$

You can simplify using log laws to either:

$\displaystyle 50\ln \left(k\left(|8-e^{-.02x}|\right)\right)$ where $\displaystyle k = \ln(C)$

$\displaystyle \ln \left(|8-e^{-.02x}|\right)^{50} + C$

Personally I'd pick the first answer

3. ## Re: Integrat with substitution

Thanks, I looked back through it and I thought it was ok... Thanks for reminding me about the constant!

Also, I'm new to the forum, I can't copy and past microsoft equation editor into the post, how do you type your equations? Does it automatically format them if you use the proper code?

4. ## Re: Integrat with substitution

$$CODE$$. Hence my final answer is: [TEX]50\ln\left(|8-e^{-.02x}|\right) + C[/TEX]

The codes for various LaTeX is given inthis thread (although the images don't work so it's either google or the PDF)

5. ## Re: Integrat with substitution

Originally Posted by wintermath
I'm new to the forum, I can't copy and past microsoft equation editor into the post, how do you type your equations? Does it automatically format them if you use the proper code?
Here is the code that $\displaystyle e^{i\pi}$ used.

[TEX]50\ln\left(|8-e^{-.02x}|\right) + C[/TEX]

[tex]50\ln \left(k\left(|8-e^{-.02x}|\right)\right) [/TEX] where [TEX]k = \ln(C)[/TEX]

[tex]\ln \left(|8-e^{-.02x}|\right)^{50} + C[/TEX]

6. ## Re: Integrat with substitution

Originally Posted by e^(i*pi)
although the images don't work so it's either google or the PDF
Actually, I believe the images are working again, thanks to our admins.

Test:

7. ## Re: Integrat with substitution

Originally Posted by Ackbeet
Actually, I believe the images are working again, thanks to our admins.

Test:

That one works. For now I'd recommend anyone who wishes to open an image does so in a new tab since for me it opens in a new tab but the back button is disabled