1. What is an Indefinite Integral?

The indefinite integral, also known as the antiderivative, of a function f(x) is a function F(x) whose derivative is f(x). It represents a family of functions differing by a constant (C).

2. How Does the Calculator Work?

The calculator uses integration rules to find antiderivatives:

Where:

• \( \int \) — Integral symbol
• \( f(x) \) — Integrand (function to integrate)
• \( dx \) — Differential indicating integration with respect to x
• \( F(x) \) — Antiderivative of f(x)
• \( C \) — Constant of integration

Explanation: The calculator applies standard integration rules like power rule, trigonometric integrals, exponential integrals, etc.

3. Importance of Indefinite Integrals

Details: Indefinite integrals are fundamental in calculus, used to find antiderivatives, solve differential equations, and calculate areas under curves (when combined with definite integrals).

4. Using the Calculator

Tips: Enter the function in terms of x using standard mathematical notation. The calculator supports basic functions like polynomials, trigonometric, exponential, and logarithmic functions.

5. Frequently Asked Questions (FAQ)

Q1: What does the +C mean in the result?
A: The +C represents the constant of integration, since the derivative of any constant is zero, and thus the antiderivative can have any constant value.

Q2: Can this calculator solve all integrals?
A: No calculator can solve all integrals symbolically. Some functions have no elementary antiderivative (e.g., e^(-x^2)).

Q3: How accurate are the results?
A: The calculator provides exact symbolic solutions when possible, not numerical approximations.

Q4: What notation should I use for exponents?
A: Use the caret symbol (^), like x^2 for x squared or e^(2x) for e to the 2x power.

Q5: Can I integrate functions with multiple variables?
A: This calculator only handles single-variable integration with respect to x.