Integral Calculator
Calculate integrals (antiderivatives) of common functions.
Find both indefinite and definite integrals with step-by-step solutions.
Integral Result
Basic Integration Rules:
| Function | Integral |
|---|---|
| x^n (n ≠ -1) | x^(n+1)/(n+1) + C |
| 1/x | ln |
| e^x | e^x + C |
| sin(x) | -cos(x) + C |
| cos(x) | sin(x) + C |
| sec²(x) | tan(x) + C |
| a × f(x) | a × ∫f(x)dx |
Key Concepts:
- Indefinite integral: The general antiderivative, includes + C
- Definite integral: Has bounds, gives a specific number (area under curve)
- Fundamental Theorem of Calculus: ∫[a to b] f(x)dx = F(b) - F(a)
What is integration? Integration is the reverse of differentiation. It calculates accumulated quantities like area, volume, and total change.