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Free Integral Calculator | pctcalc.org - Step-by-Step Solutions

Online Integral Calculator

Calculate integrals instantly with step-by-step solutions. Supports indefinite and definite integrals using the powerful SymPy engine.

Integral Calculator

Calculate integrals using SymPy

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Examples:

Basic Polynomials

Rational Functions

Trigonometric Functions

Exponential Functions

Logarithmic Functions

Inverse Trigonometric

Square Roots

Products (Integration by Parts)

Composite Functions

Hyperbolic Functions

Powers with Different Bases

More Complex Examples

Special Functions

Features

✨ Indefinite Integrals

Calculate indefinite integrals with constant of integration. Get symbolic results in LaTeX format.

📊 Definite Integrals

Compute definite integrals with custom bounds. Get both symbolic and numeric results.

⚡ Fast & Accurate

Powered by SymPy, a world-class symbolic mathematics library. Results are mathematically accurate.

🎯 Step-by-Step Solutions

View detailed results with symbolic expressions, LaTeX formatting, and numeric approximations.

How to Use

1. Enter Your Expression

Type your mathematical expression using standard notation:

  • x^2 for x²
  • sin(x) for trigonometric functions
  • exp(x) for eˣ
  • log(x) for natural logarithm
  • sqrt(x) for √x

2. Select Integration Type

Choose between:

  • Indefinite Integral: Indefinite Integral: Calculate ∫f(x)dx
  • Definite Integral: Definite Integral: Calculate ∫ₐᵇf(x)dx with bounds

3. Click Calculate

Press the calculate button to get your result in LaTeX format with detailed steps.

Supported Functions

Basic Operations

  • +, -, *, /, **
  • Parentheses: ( )

Trigonometric

  • sin, cos, tan
  • asin, acos, atan
  • sinh, cosh, tanh

Exponential & Log

  • exp, log, ln
  • sqrt, cbrt

Constants

  • pi (π)
  • E (e)

Frequently Asked Questions

Why is the first load slow?

The calculator needs to download and initialize Pyodide (a Python runtime) and SymPy library, which is about 10-15MB. This only happens once per session, and subsequent calculations are fast.

What types of integrals are supported?

The calculator supports both indefinite integrals (with constant C) and definite integrals (with custom bounds). It can handle polynomials, trigonometric functions, exponentials, logarithms, and many other mathematical functions.

What if my expression can't be solved?

Some integrals don't have closed-form solutions. In such cases, SymPy will return the original expression, indicating that a closed-form solution doesn't exist. You may need to use numerical integration methods for these cases.

How do I enter special symbols?

Use standard ASCII notation: ^ for power, pi for π, sqrt for √. The calculator automatically converts these to the correct format.