Answer by taking a quote from the following article:

A Night at the Opera is the fourth studio album by the British rock band Queen, released on 21 November 1975 by EMI Records in the United Kingdom and by Elektra Records in the United States. Produced by Roy Thomas Baker and Queen, it was the most expensive album ever recorded at the time of its release. The album takes its name from the Marx Brothers film of the same name, which the band watched one night at the studio complex when recording. A Night at the Opera incorporates a wide range of styles, including ballads, songs in a music hall style, hard rock tracks and progressive rock influences.

"Bohemian Rhapsody" was written by Mercury with the first guitar solo composed by May. All piano, bass and drum parts, as well as the vocal arrangements, were thought up by Mercury on a daily basis and written down "in blocks" (using note names instead of sheets) on a phonebook. The other members recorded their respective instruments with no concept of how their tracks would be utilised in the final mix. The famous operatic section was originally intended to be only a short interlude of "Galileos" that connected the ballad and hard rock portions of the song.  The interlude is full of "obscure classical characters: Scaramouche, a clown from the commedia dell'arte; astronomer Galileo; Figaro, the principal character in Beaumarchais' The Barber of Seville and The Marriage of Figaro...Beelzebub; identified in the Christian New Testament as Satan, Prince of Demons, but in Arabic as "Lord of the Flies". Also in Arabic the word Bismillah', which is a noun from a phrase in the Qur'an; "Bismi-llahi r-rahmani r-rahiim", meaning "In the name of God, most gracious, most merciful".  During the recording, the song became affectionately known as "Fred's Thing" to the band, and the title only emerged during the final sessions.  Despite being twice as long as the average single in 1975 and garnering mixed critical reviews initially, the song became immensely popular, topping charts worldwide (where it remained for an unprecedented nine weeks in the UK) and is widely regarded as one of the most significant rock songs in history.  After Freddie Mercury's death, the song was rereleased as a double A-side to "These Are The Days Of Our Lives" on 9 December 1991 in the UK and September 5, 1991, in US.

Who wrote Bohemian Rhapsoday?
"Bohemian Rhapsody" was written by Mercury