docs: Add W&B Weave integration documentation (#1743)

docs/logfire.md

@@ -238,6 +238,127 @@ print(result.output)
 #> Paris
 ```
 
+## Using W&B Weave
+
+[W&B Weave](https://weave-docs.wandb.ai/) is an observability platform by Weights & Biases that can receive and visualize OpenTelemetry traces from your PydanticAI applications.
+
+Since PydanticAI uses OpenTelemetry for instrumentation, you can send your agent and tool traces to Weave for visualization and analysis.
+
+### Setup
+
+To use W&B Weave with PydanticAI, you'll need to install the required OpenTelemetry dependencies:
+
+```bash
+pip install opentelemetry-sdk opentelemetry-exporter-otlp-proto-http
+```
+
+### Configuring OTEL for Weave
+
+Configure OpenTelemetry to send traces to Weave by setting up a tracer provider and exporter:
+
+```python
+import base64
+import os
+from opentelemetry.exporter.otlp.proto.http.trace_exporter import OTLPSpanExporter
+from opentelemetry.sdk import trace as trace_sdk
+from opentelemetry.sdk.trace.export import SimpleSpanProcessor
+
+# Load sensitive values from environment variables
+WANDB_BASE_URL = "https://trace.wandb.ai"
+PROJECT_ID = os.environ.get("WANDB_PROJECT_ID")  # Your W&B entity/project name e.g. "myteam/myproject"
+WANDB_API_KEY = os.environ.get("WANDB_API_KEY")  # Your W&B API key (can be found at https://wandb.ai/authorize)
+
+OTEL_EXPORTER_OTLP_ENDPOINT = f"{WANDB_BASE_URL}/otel/v1/traces"
+AUTH = base64.b64encode(f"api:{WANDB_API_KEY}".encode()).decode()
+
+OTEL_EXPORTER_OTLP_HEADERS = {
+    "Authorization": f"Basic {AUTH}",
+    "project_id": PROJECT_ID,
+}
+
+# Create the OTLP span exporter with endpoint and headers
+exporter = OTLPSpanExporter(
+    endpoint=OTEL_EXPORTER_OTLP_ENDPOINT,
+    headers=OTEL_EXPORTER_OTLP_HEADERS,
+)
+
+# Create a tracer provider and add the exporter
+tracer_provider = trace_sdk.TracerProvider()
+tracer_provider.add_span_processor(SimpleSpanProcessor(exporter))
+```
+
+!!! tip "Secure your credentials"
+    Store sensitive values like your API key in environment variables or a secure credentials manager, not directly in your code.
+
+### Tracing PydanticAI agents
+
+To trace your agents, pass an `InstrumentationSettings` object with your configured tracer provider:
+
+```python
+from pydantic_ai import Agent
+from pydantic_ai.models.instrumented import InstrumentationSettings
+
+# Create a PydanticAI agent with OTEL tracing
+agent = Agent(
+    "openai:gpt-4o",
+    instrument=InstrumentationSettings(tracer_provider=tracer_provider),
+)
+
+result = agent.run_sync("What is the capital of France?")
+print(result.output)
+#> Paris
+```
+
+### Tracing tools
+
+When your agent uses tools, both the agent calls and tool executions will be traced:
+
+```python
+from pydantic_ai import Agent
+from pydantic_ai.models.instrumented import InstrumentationSettings
+
+# Create an agent with a system prompt and OTEL tracing
+agent = Agent(
+    "openai:gpt-4o",
+    system_prompt=(
+        "You are a helpful assistant that can multiply numbers. "
+        "When asked to multiply numbers, use the multiply tool."
+    ),
+    instrument=InstrumentationSettings(tracer_provider=tracer_provider),
+)
+
+# Define a tool
+@agent.tool_plain
+def multiply(a: int, b: int) -> int:
+    """Multiply two numbers."""
+    return a * b
+
+# Ask the agent to use the tool
+result = agent.run_sync("What is 7 multiplied by 8?")
+print(result.output)
+#> 56
+```
+
+### Instrumenting all agents with Weave
+
+To apply Weave tracing to all agents in your application:
+
+```python
+from pydantic_ai import Agent
+from pydantic_ai.models.instrumented import InstrumentationSettings
+
+# Set up default instrumentation for all agents
+Agent.instrument_all(InstrumentationSettings(tracer_provider=tracer_provider))
+
+# Now, any new agent will use this instrumentation by default
+agent = Agent("openai:gpt-4o")
+result = agent.run_sync("What is the capital of France?")
+print(result.output)
+#> Paris
+```
+
+For more information, see the [W&B Weave documentation on PydanticAI integration](https://weave-docs.wandb.ai/guides/integrations/pydantic_ai).
+
 ## Advanced usage
 
 ### Configuring data format