Question

what are the integral of dx/(e^x +1) and dx/((e^x + 1)e^2x)

Answer 1

Notice that
\[ \frac{1}{e^x+1} = \frac{e^x + 1}{e^x+1} - \frac{e^x}{e^x+1} \]

Answer 2

but im no used to these seperation of fractions. really how you know when to separate fractions?

Answer 3

I'm not using partial fractions; I'm just trying to write 1/(e^x+1) as the sum of functions we can integrate.

Clearly the first term (e^x+1)/(e^x+1) = 1, which you can integrate. Look now at the second term and see why you can integrate that.

Answer 4

i know the answer now thnx. but im not sure if i can do it in tst ^.^

Answer 5

That's why you practice and see different examples, to help build up your personal tool kit.