a) Use the proof of the integral test to show that $\ln(n!)\ge n\ln(n)-n+1$ for $n>1$
b) Use part (a) to show that $\ln(n!)\ge n\ln(n)$ for $n\ge 10$
I was able to solve part a) but not completely. The proof says that $\sum_{k=1}^{n} \ln(n) \ge \int_{1}^{n+1} \ln(x) \mathrm{d}x$ not $\int_{1}^{n}\ln(x) \mathrm{d}x$.
Also, assuming part a), I don't see how to proceed in part b) to get the result for $n\ge10$.