What functions does this calculator support?

It supports polynomials (e.g. x^3, 5x^2), constants, trigonometric functions (sin, cos, tan, sec, csc, cot), exponential functions (e^x, a^x), and natural/common logarithms. Combinations of supported terms using + and - are handled automatically.

What is the constant C in the result?

Since differentiation removes constants, every indefinite integral has an arbitrary constant C added to represent all possible antiderivatives of a given function. In definite integration, C cancels out.

Why does the calculator not handle all functions?

This tool uses a rule-based lookup table for common function patterns. Functions that require advanced techniques like integration by parts, partial fractions, or trigonometric substitution are beyond the scope of this calculator.

What is the power rule for integration?

For any term ax^n (where n is not -1), the integral is a * x^(n+1) / (n+1) + C. For example, the integral of 3x^2 is x^3 + C.

How do I enter a function with a coefficient?

Write the coefficient directly before the variable, e.g. "3x^2 + 2x - 5" or "4sin(x) + 2e^x". The calculator will apply the constant multiple rule automatically.

Does this tool compute definite integrals?

No. This tool computes indefinite integrals only. For definite integrals, take the antiderivative result, evaluate it at the upper and lower bounds, and subtract.

Indefinite Integral Calculator

Name: Indefinite Integral Calculator
Availability: InStock
Author: Nham Vu

Enter a function and see its indefinite integral with a step-by-step breakdown of the integration rules applied.

Enter a Function

f(x) =

Use ^ for powers, * for multiplication (optional). Separate terms with + or -.

Quick Examples

Enter a function on the left to see its integral.

Copied!

Summary

Enter a function and see its indefinite integral with a step-by-step breakdown of the integration rules applied.

How it works

Type your function into the input field (e.g. 3x^2, sin(x), e^x).
The calculator parses the expression and identifies each term.
Standard integration rules are applied: power rule, constant multiple, sum/difference, trig rules, and exponential/log rules.
The result is displayed with a + C constant of integration appended.
A step-by-step breakdown shows which rule was applied to each term.
Use the Copy button to copy the result to your clipboard.

Use cases

Check antiderivative answers while studying calculus.
Quickly find the integral of polynomial expressions.
Verify trigonometric and exponential antiderivatives.
Understand which integration rule applies to each function type.
Help students learn integration rules step by step.
Use as a reference when solving physics or engineering integrals.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu