Answer
\[ =-\dfrac{(2m+1)^{-2}}{2} +C \]
Work Step by Step
In order to integrate this function, we have to use a «u» substitution.
But first rewrite the function:
\[ \int 2(2m+1)^{-3} dm \]
Choose an u, derivate it:
$ u = 2m+1 $
$ du = 2dm$
Then substitute:
\[ =\int u^{-3} du \]
Then integrate
\[ =\dfrac{u^{-2}}{-2}+C \]
And undo the substitution:
\[ =-\dfrac{(2m+1)^{-2}}{2} +C \]
