# Integration help

• April 24th 2006, 08:57 PM
charps43
Integration help
I'm having trouble remembering how to take the integral of

f(x) = (1 - ax) / bx , where a and b are constants.

Any help would be good.

Thanks,

Brett
• April 24th 2006, 09:21 PM
earboth
Quote:

Originally Posted by charps43
I'm having trouble remembering how to take the integral of
f(x) = (1 - ax) / bx , where a and b are constants.
Any help would be good.
Thanks,
Brett

Hello,

1. Expand the RHS of the equation:
$f(x)=\frac{1-ax}{bx}=\frac{1}{b} \cdot \frac{1}{x} - \frac{ax}{bx}$. Don't forget to simplify the 2nd summand.

$\int \left( \frac{1}{b} \cdot \frac{1}{x} - \frac{a}{b} \right) dx=\frac{1}{b} \cdot \ln(x)- \frac{a}{b} \cdot x + C$

Greetings

EB