I am having trouble integrating the equation $\frac{dN}{dlogM} = C\left(\frac{M}{M_{br}}\right)^n$. I just need it between two limits, say $M_{l}$ and $M_{h}$. Sorry for a remedial question, it has been a long time since I have had to do something like this (if I have in the past). How do I convert the limits/the function? These are all $\log_{10}$, not natural logs.
Here is where I am at:
$ N = \int_{M_{l}}^{M_{h}} C \left(\frac{M}{M_{br}}\right)^n dlogM $
Substitute $\frac{d\log_{10}M}{dM} =\frac{1}{M\ln10}$
$ N = \int_{M_{l}}^{M_{h}} C \left(\frac{M}{M_{br}}\right)^n \frac{1}{M\ln 10}dM. $
Then some simplifying and solving. Am I wrong anywhere? Do I need to do anything to the limits ($M_h,M_l$)? Thank you!