When a pair of smiling Mormon missionaries appear at your door, they will have a special request for you: "pray to know that the Book of Mormon is true." To these Mormons, who have already done so, this test is perfectly reasonable. The problem is that this test doesn't come from the Bible, it comes from Moroni 10:4.
The source of this test matters, because we humans are terrible at interpreting answers to prayer. This is because our heart is deceitful above all things (Jeremiah 17:9), a fact Satan is not shy about exploiting.
Before I converted to Christianity, I had become rather ensnared by the LGBT ideology. I was actively gay, seeking a boyfriend. That was until I got into a debate with an agnostic, who showed me that the Bible is against homosexuality. Mormonism is also against homosexuality. You can probably see where I'm going with this.
At first, there was a lot of resistance in my heart. Did God really want me to give up such a large part of my identity? After all, He loves me, right? So surely He wouldn't ask something so harsh of me. So I prayed about it. The result: I became more confident in my homosexuality. I "knew in my heart" that those verses must have meant something else, and that even if homosexuality is a sin, God loves me, and will forgive me for it anyway.
If you think merely praying is a useful test for truth, you either don't know God, or don't know Satan. In reality, prayer on its own is very irresponsible. This is because Satan and his minions are capable of mimicking good (2 Corinthians 11:14-15), and God doesn't answer prayers said with wrong motives (James 4:3). It's even possible that Muhammad and Joseph Smith saw real angels. With such deceptive power, it's not a stretch to suggest that if a demon inspired the Book of Mormon, that same demon will testify that it's true to anyone who prays about it. And God, having given us everything we need to resist such deception (2 Timothy 3:16-17), will justly reward those who forgo its use.
Most Mormons will probably admit it was stupid of me to pray about homosexuality. It wasn't God who told me homosexuality is ok, it was my own desire. God has already given His opinions about homosexuality in various places in the Scriptures. He calls it an unnatural abomination (Romans 1:26-27) which prevents one from entering His Kingdom (1 Corinthians 6:9-10). In the same way, God makes His Gospel very clear in the Scriptures. I don't need to pray about the Book of Mormon any more than I need to pray about the Qur'an. I just need to do what the Bereans did in Acts 17:11: search the Scriptures daily to find out if these things are so.
While The Book of Mormon may pass the "burning in the bosom" test of Moroni 10:4, it fails to hold up when compared to God's previous revelations. Where, then, does a Mormon's testimony come from? Evidently, from the same spirit that inspired the Book of Mormon from which this test comes. That spirit is not a Holy one, but rather, as Paul says in Galatians 1:8, it is anathema.