newton

Integrate

integrate

Read-onlyIdempotent

Find the indefinite integral of an expression with respect to x. Input algebraic notation (e.g., "x^2"). Returns antiderivative with constant C.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`expression`	Yes	Expression to integrate (e.g., "x^2", "cos(x)", "x^3+x")

Output Schema

TableJSON Schema

Name	Required	Description
`input`	Yes	The input expression
`result`	Yes	Antiderivative expression with constant C or null
`operation`	Yes	Operation name (integrate)

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedMay 8, 2026

changedOutput schema / (root)

Previous value: -nullNew value: +{
+  "properties": {
+    "input": {
+      "description": "The input expression",
+      "type": "string"
+    },
+    "operation": {
+      "description": "Operation name (integrate)",
+      "type": "string"
+    },
+    "result": {
+      "description": "Antiderivative expression with constant C or null",
+      "type": [
+        "string",
+        "null"
+      ]
+    }
+  },
+  "required": [
+    "operation",
+    "input",
+    "result"
+  ],
+  "type": "object"
+}

Changed1 schema field changedMay 6, 2026

addedInput schema / examples

Added value: +[
+  {
+    "expression": "x^2"
+  },
+  {
+    "expression": "cos(x)"
+  }
+]

First observedApr 14, 2026

TDQS

A4.4/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already indicate a safe read-only, idempotent operation, so the description's additional details are valuable. It discloses the return behavior (antiderivative with constant C) and the integration variable, adding context beyond annotations without contradicting them.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is two sentences, front-loaded with the primary purpose, and each sentence adds necessary information. It is concise, well-structured, and contains no redundant filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's simplicity (one parameter, output schema present), the description adequately covers the operation, input expectations, and return behavior. It does not mention edge cases or error handling, but these are not critical for such a straightforward tool with rich annotations and schema.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema fully documents the 'expression' parameter with examples, but the description adds meaning by specifying 'algebraic notation' and 'with respect to x', which clarifies the expected input format and the role of the variable. This goes beyond the schema's basic type and examples.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's function with a specific verb ('Find') and resource ('indefinite integral of an expression'), and specifies the variable of integration ('with respect to x'). This distinguishes it from sibling math tools like derive, factor, and simplify, making the purpose unambiguous.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides clear context on how to use the tool (input algebraic notation, integration with respect to x) and what it returns. However, it does not explicitly mention when to use this tool over alternatives like derive or factor, though the clarity of purpose makes the appropriate usage strongly implied.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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