Indefinite Integral Calculator
An indefinite integral calculator helps compute antiderivatives of mathematical functions. It's essential for calculus students and professionals to solve integration problems quickly, verify solutions, and understand complex relationships between functions. This tool eliminates manual calculation errors and provides instant results, making it invaluable for engineering, physics, and mathematics applications.
Calculator
Integration Formula
The basic indefinite integral formula is ∫f(x)dx = F(x) + C, where F'(x) = f(x) and C is the constant of integration. Common rules include power rule (∫x^n dx = x^(n+1)/(n+1) + C), trigonometric integrals, and exponential rules.
How to Use
1. Enter function in input box (e.g., 3x^2 + 2x)
2. Click Calculate button
3. View result with constant of integration
4. Use Clear button to reset
Supported functions: polynomials, sin, cos, tan, exp, sqrt
Derivation Process
Indefinite integrals are derived by reversing differentiation through integration rules. The calculator uses symbolic computation to apply:
1. Power rule for polynomial terms
2. Trigonometric identities for sin/cos functions
3. Exponential rules for e^x terms
4. Sum rule for combining terms
Results include integration constant (C) as fundamental theorem requires.
Common Integrals Table
| Function | Integral |
|---|---|
| x^n | x^(n+1)/(n+1) + C |
| sin(x) | -cos(x) + C |
| cos(x) | sin(x) + C |
| e^x | e^x + C |
| 1/x | ln|x| + C |