間違える vs 間違う

It seems like both of these words can be transitive and mean “to make a mistake.”

So for the example sentence:

大事な事を間違うという経験を活かして、注意深い人間になるつもりです。

How would I know which word to use? Or would either be acceptable, and maybe Bunpro should warn me instead of marking it wrong?

Thanks!

I was also curious about this a while ago. I don’t know about bunpro, but from my understanding “machigau” used to basically be intransitive only while “machigaeru” was the transitive form. However, “machigau” was increasingly used as a transitive verb. I think that technically hardcore grammar purists would say using “machigau” transitively is incorrect, but it became commonly used and accepted.