"method of investigating" is correct and usable in written English.
You could use it when you want to refer to a particular technique for obtaining information or data. For example, "The detective employed a unique method of investigating the crime."
Gould never embraced cladistics as a method of investigating evolutionary lineages and process, possibly because he was concerned that such investigations would lead to neglect of the details in historical biology, which he considered all-important.
Seismic survey, method of investigating subterranean structure, particularly as related to exploration for petroleum, natural gas, and mineral deposits.
In November, Congress passed a bill requiring the Defense Department to review its method of investigating military suicides.
Meanwhile, a Viennese physician, Leopold Auenbrugger, discovered another method of investigating diseases of the chest, that of percussion.
Post-mortem radiological imaging is a potential alternative method of investigating perinatal loss.
It influenced the mid-20th century conception of philosophy as a critical method of investigating problems and clarifying communication rather than as a universal synthesis of knowledge.
The paper presents an analytic method of investigating impacting mechanical systems.
These measurements also suggest the possibility of a new method of investigating structural characteristics.
This paper describes a novel method of investigating the chemical behavior of both analyte and quencher molecules in the FPD.
She added that Microsoft "is very interested in working with the F.B.I. to develop the right method of investigating and prosecuting spammers," but that "at this point the company has not committed to any particular strategy like the D.M.A.'s".
The nay-sayers insist loudly that they're "climate sceptics", but this is a calculated misnomer – scientific scepticism is the method of investigating whether a particular hypothesis is supported by the evidence.
