"successfully represent" is correct and usable in written English.
It can be used when describing someone or something accurately or effectively, often in a professional or legal context. Example: The attorney successfully represented her client in court, convincing the jury of their innocence.
At Paul Weiss, he moved quickly through the ranks, working with two of the firm's leading partners to successfully represent Pennzoil in the landmark case against Texaco, which tried to scuttle its deal with Getty Oil.
She's named her other sculptures "Untitled Forcefield," but only two successfully represent the push-me/pull-you concept in physics, which posits that the introduction of a new object into a stable playing ground will repel or attract the other objects until equilibrium is established.
These systems are being used to successfully represent different kinds of engineering systems.
It should be noted that the learned atomic spectra often could not successfully represent the spectral characteristic of each pitch.
Assessment of salivary immunoglobulins and antimicrobial proteins has been shown to successfully represent the effects of exercise on mucosal immunity.
The procedure is able to successfully represent systems with similar macroscopic properties, i.e. density and viscosity ratios approaching unity, and a broad range of interfacial tensions.
Arguably, Rome is more successfully represented in films.
Mr. Ciampoli has successfully represented several candidates contesting ballot results, including Senator Spano earlier this year.
In 2001 he successfully represented a Haitian immigrant, Abner Louima, who was brutally assaulted by policemen.
Ted Poretz, the Manhattan lawyer who successfully represented the co-op at 136 East 56th Street, agreed.
Mr. Kohn successfully represented Linda Tripp, who helped expose the Monica Lewinsky scandal of the Clinton years.
