Integrated　microwave　photonics　(MWP)　is　an　intriguing　technology　for　the　generation,　transmission　and　manipulation　of　microwave　signals　in　chip-scale　optical　systems1,2.　In　particular,　ultrafast　processing　of　analogue　signals　in　the　optical　domain　with　high　fidelity　and　low　latency　could　enable　a　variety　of　applications　such　as　MWP　filters3-5,　microwave　signal　processing6-9　and　image　recognition10,11.　An　ideal　integrated　MWP　processing　platform　should　have　both　an　efficient　and　high-speed　electro-optic　modulation　block　to　faithfully　perform　microwave-optic　conversion　at　low　power　and　also　a　low-loss　functional　photonic　network　to　implement　various　signal-processing　tasks.　Moreover,　large-scale,　low-cost　manufacturability　is　required　to　monolithically　integrate　the　two　building　blocks　on　the　same　chip.　Here　we　demonstrate　such　an　integrated　MWP　processing　engine　based　on　a　4　inch　wafer-scale　thin-film　lithium　niobate　platform.　It　can　perform　multipurpose　tasks　with　processing　bandwidths　of　up　to　67　GHz　at　complementary　metal-oxide-semiconductor　(CMOS)-compatible　voltages.　We　achieve　ultrafast　analogue　computation,　namely　temporal　integration　and　differentiation,　at　sampling　rates　of　up　to　256　giga　samples　per　second,　and　deploy　these　functions　to　showcase　three　proof-of-concept　applications:　solving　ordinary　differential　equations,　generating　ultra-wideband　signals　and　detecting　edges　in　images.　We　further　leverage　the　image　edge　detector　to　realize　a　photonic-assisted　image　segmentation　model　that　can　effectively　outline　the　boundaries　of　melanoma　lesion　in　medical　diagnostic　images.　Our　ultrafast　lithium　niobate　MWP　engine　could　provide　compact,　low-latency　and　cost-effective　solutions　for　future　wireless　communications,　high-resolution　radar　and　photonic　artificial　intelligence.　An　integrated　lithium　niobate　photonic　processing　engine　performs　integration　and　differentiation　of　analogue　signals,　solves　ordinary　differential　equations,　generates　ultra-wideband　microwave　signals　and　detects　edges　in　images.