In an English textbook, I found the following sentence.
The Swiss tunnel took 17 years to build.
A tunnel is supposed to be built, so I think the sentence could be re-written.
The Swiss tunnel took 17 years to be built.
According to a native speaker, the first sentence is much better.
Should I use to build, to be built, or to have built in that sentence?
In your case , a) is indeed much better, because the tunnel itself took no part in the construction; it took [the tunnelling company, with their engineers and tunnelling machinery] 17 years to build it. A coral reef, on the other hand, might take some time to be built equally as well as some time to build.
The first two suggested sentences are both grammatical and common. In this case, the meaning of the sentences is the same, but there are a couple of reasons to prefer 1.
First, sentence 1 is more concise. "To be built" adds extra verbiage without changing the meaning of the sentence.
Second, as Lambie points out, sentence 2 is passive. Passive sentences have a less immediate feel, and can give the impression of talking around the issue of who performed the action.
"The Swiss tunnel took 17 years to have built" is not a natural way to phrase this sentence.
to build and to be built have pretty much the same meaning.
The first sentence is an active sentence, while the second is a passive sentence.
So you can think of it like this:
In the first sentence, the people who are building the tunnel are in the focus, while in the second sentence you're putting the focus on the tunnel.
Both aren't wrong and both say essentially the same thing, but the second sentence is pointing out the tunnel more than the first.
The tunnel is the object, not the subject, of "build", so "have built" is definitely not correct. "to be built" can give more of a sense of "time until building", whereas "to build" gives more of a sense of "time spent building". For instance, if planning on the bridge started in 2000, but construction didn't start until 2003, and construction ended in 2020, then one could say "The bridge took 17 years to build", but "The bridge took 20 years to be built". Those two phrasings do overlap, however, so either one could be used for either meaning, but those are the main meanings. I find "It took 17 years to build the bridge" and "It took 20 years before the construction of the bridge was finished", respectively, to be more natural, though.
It's quite difficult to substantiate: "According to a native speaker, "a." is much better," but in this case, the Ngram program, crude as it is, actually provides some useful material.
Both forms are possible (and both are grammatically correct). However, according to Ngrams "is built" is much the commoner of the two variants, so could be considered, if not "much better", at least the preferred one in printed texts:
