Integrating a Constant Divided by a Linear Function of x

[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...

 

[quantumdude]

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

 

[elecninja]

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

 

[Mark44]

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
$$\int \frac{3}{100+2t}$$ which is 3/2 ln(100+2t).

Corrected your LaTeX. You had "fract" instead of "frac".

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.