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Graphene has unique electrical and mechanical properties which can pave the way for new types of devices for microwave applications. However, emerging technologies often have problems with yield and still considerable variation in device parameters cause great challenges for circuit design. In this paper, we present the design and development of an integrated graphene FET amplifier addressing this challenge. A representative graphene FET was selected from a set of devices and then the input and output matching circuits were designed using the negative-image technique. The two-finger GFET with a gate length of 0.5&#x00A0;<inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m exhibit a typical <inline-formula><tex-math notation="LaTeX">$f_T$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$f_{max}$</tex-math></inline-formula> of 35 GHz and 37 GHz, respectively. The integrated graphene FET amplifier was fabricated on a high-resistivity silicon substrate together with thin film capacitors, airbridges, and spiral inductors. A record high gain of <inline-formula><tex-math notation="LaTeX">$4.2\,$</tex-math></inline-formula>dB at <inline-formula><tex-math notation="LaTeX">$10.6\,$</tex-math></inline-formula>GHz was measured for a single transistor amplifier stage and agrees well with simulations. These results indicate significant progress towards active microwave circuits based on emerging 2D materials.