# Integrating a/u

1. Mar 9, 2009

### alpha120

Okay well, I looked through my calculus notes and textbook and I can't find what to do when you are integrating a function of the type a/u where a is a constant and u is some linear function of x. I know that the integral of 1/x is ln(x) but what about when you have something like
$$\int \fract{3}{100+2t}$$ which is 3/2 ln(100+2t).

If I recall the derivative of ln(u) is u'/u, so I assume it must somehow be like that. I am sure I learned how to integrate it somewhere along the road... must've been asleep that class or something though...

2. Mar 9, 2009

### Tom Mattson

Staff Emeritus
You need to to a u-substitution. Let u equal the denominator, and go from there.

3. Mar 9, 2009

### elecninja

Nvm. Apparently I couldn't see the code right.

Last edited: Mar 9, 2009
4. Mar 9, 2009

### Staff: Mentor

Also, you should get in the habit of including the differential, dt in this case. If you don't, it will definitely come back and bite you very soon.