Punctuation of successive imperative sentences

I was wondering whether the following sentences are punctuated properly:

To show this, multiply the ODE by x; integrate over x, and perform repeated integration by parts, it then follows that: f=0.


‘To show this’ is adverbial, so the first comma makes sense.

Then there is a list of imperatives. Commas are fine for separating them. Do not mix commas and semicolons at the same nesting level. (You might use both semicolons and commas if some of the list items have ‘parenthetical’ nesting.)

‘It then follows that …’ is not part of the list. It should be a new sentence (or at least separated by a semicolon).

Source : Link , Question Author : Saj_Eda , Answer Author : AmI

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