One of 'e' Logarithm Properties

The most common logarithm proofs that you can find in most books,internet,wiki,and teachers might have taught you is this.....
Prove

Let
Then

Therefore,
. This completes the proof

I have another way of proofing this with calculus ...

Let the variable in
Then and the limits of integration and and
Hence,

.
The property is proved in different way! Happy proofing!