Make it clearer how to instrument all OpenAI clients (#1135)

Author: alexmojaki

docs/integrations/llms/anthropic.md

@@ -3,8 +3,8 @@ integration: logfire
 ---
 # Anthropic
 
-**Logfire** supports instrumenting calls to [Anthropic](https://github.com/anthropics/anthropic-sdk-python)
-with one extra line of code.
+**Logfire** supports instrumenting calls to [Anthropic](https://github.com/anthropics/anthropic-sdk-python) with the [`logfire.instrument_anthropic()`][logfire.Logfire.instrument_anthropic] method, for example:
+
 
 ```python hl_lines="7"
 import anthropic
@@ -13,7 +13,8 @@ import logfire
 client = anthropic.Anthropic()
 
 logfire.configure()
-logfire.instrument_anthropic(client)  # (1)!
+logfire.instrument_anthropic()  # instrument all Anthropic clients globally
+# or logfire.instrument_anthropic(client) to instrument a specific client instance
 
 response = client.messages.create(
     max_tokens=1000,
@@ -24,10 +25,6 @@ response = client.messages.create(
 print(response.content[0].text)
 ```
 
-1. If you don't have access to the client instance, you can pass a class (e.g. `logfire.instrument_anthropic(anthropic.Anthropic)`), or just pass no arguments (i.e. `logfire.instrument_anthropic()`) to instrument both the `anthropic.Anthropic` and `anthropic.AsyncAnthropic` classes.
-
-_For more information, see the [`instrument_anthropic()` API reference][logfire.Logfire.instrument_anthropic]._
-
 With that you get:
 
 * a span around the call to Anthropic which records duration and captures any exceptions that might occur

docs/integrations/llms/openai.md

@@ -6,8 +6,7 @@ We support instrumenting both the [standard OpenAI SDK](https://github.com/opena
 
 ## OpenAI SDK
 
-Logfire supports instrumenting calls to OpenAI with one extra line of code, here's an example of instrumenting
-the OpenAI SDK:
+**Logfire** supports instrumenting calls to OpenAI with the [`logfire.instrument_openai()`][logfire.Logfire.instrument_openai] method, for example:
 
 ```python hl_lines="7"
 import openai
@@ -16,7 +15,8 @@ import logfire
 client = openai.Client()
 
 logfire.configure()
-logfire.instrument_openai(client)  # (1)!
+logfire.instrument_openai()  # instrument all OpenAI clients globally
+# or logfire.instrument_openai(client) to instrument a specific client instance
 
 response = client.chat.completions.create(
     model='gpt-4',
@@ -28,10 +28,6 @@ response = client.chat.completions.create(
 print(response.choices[0].message)
 ```
 
-1. If you don't have access to the client instance, you can pass a class (e.g. `logfire.instrument_openai(openai.Client)`), or just pass no arguments (i.e. `logfire.instrument_openai()`) to instrument both the `openai.Client` and `openai.AsyncClient` classes.
-
-_For more information, see the [`instrument_openai()` API reference][logfire.Logfire.instrument_openai]._
-
 With that you get:
 
 * a span around the call to OpenAI which records duration and captures any exceptions that might occur