How to integrate fraction?

Question

How do you integrate
1/(100+t) dt

Answer 1

Use the substitution method.

The original function is:

1/(100 + t) dt

let u = 100 + t

then differentiate u:

du/dt = 1
du = dt

From these information, you can reword the function again into:

1/u du

Now, you'll need to remember a formula where the integral of 1/x = ln |x|
This applies here, where you can integrate this function into:

ln |u| + C

But u = 100 + t,
so the answer will equal to:

ln |100 + t| + C --> finished.