Question

Why is the integral of 1/(2x+1) =.5ln(2x+1) and not just ln(2x+1)

Answer 1

Try differentiating ln(2x+1). Don't forget the chain rule. Note the 2 in the numerator.

That .5 cancels out the 2.

Answer 2

hmm ic.

Answer 3

or to say it this way:

\[\int\limits \frac{1}{u} du = \ln u\]

in your case u = 2x+1 and du = 2 dx

you need 2 dx
so you write it like this
\[ \frac{1}{2} \int \frac{1}{2x+1} 2 dx \]

Answer 4

alrite, thanks.