Learn Italian: L'ispettore stava indagando su un crimine. - The inspector was investigating a crime.

Both are grammatically correct and translate to "was investigating." However, using the past progressive (stava + indagando) emphasizes that the action was right in the middle of happening at that exact moment in the past. It highlights the ongoing process of the investigation.

How is the indagando part formed?

Indagando is the gerund form of the verb indagare (to investigate). For verbs ending in -are, you drop the -are and add -ando. This works just like adding "-ing" in English.

Why is the preposition su used here? In English, we just say "investigating a crime."

In Italian, the verb indagare (to investigate) doesn't usually connect directly to the thing being investigated. Instead, it is followed by the preposition su (on/about). Literally, the sentence says the inspector was investigating "on" a crime.

How can I tell if crimine is masculine or feminine since it ends in -e?

You can tell it is masculine by looking at the indefinite article right before it: un. If the word were feminine, the article would be una (or un' because of a starting vowel). Since words ending in -e can be either gender, checking the article is the best way to know!