1. What is an Antiderivative?

An antiderivative, also known as an indefinite integral, is a function whose derivative is the original function. It represents the reverse process of differentiation and is fundamental to integral calculus.

2. How Does the Calculator Work?

The calculator uses integration techniques to find:

Where:

• \( f(x) \) — The function to integrate
• \( dx \) — Differential element
• \( \int \) — Integral symbol representing the antiderivative

Explanation: The calculator applies integration rules such as power rule, trigonometric integrals, exponential integrals, and substitution methods to find the antiderivative.

3. Importance of Antiderivative Calculation

Details: Antiderivatives are essential for solving differential equations, calculating areas under curves, determining accumulated quantities, and various applications in physics, engineering, and economics.

4. Using the Calculator

Tips: Enter the mathematical function f(x) using standard notation. Use common functions like sin(x), cos(x), exp(x), ln(x), and follow proper mathematical syntax.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between antiderivative and definite integral?
A: An antiderivative is a function (indefinite integral), while a definite integral calculates the numerical value of the area under the curve between two points.

Q2: Can all functions be integrated?
A: While many functions have antiderivatives, some functions (like e^(-x²)) don't have elementary antiderivatives but can be expressed using special functions.

Q3: What is the constant of integration?
A: Since differentiation eliminates constants, antiderivatives include an arbitrary constant C to account for all possible functions with the same derivative.

Q4: How accurate is the calculator?
A: The calculator uses symbolic integration algorithms to provide exact antiderivatives when possible, following standard mathematical rules and techniques.

Q5: What types of functions can I input?
A: You can input polynomial, trigonometric, exponential, logarithmic, and rational functions, as well as combinations of these using proper mathematical syntax.