The Integral Calculator computes indefinite integrals (antiderivatives) of mathematical functions. It handles polynomials, trigonometric functions, exponentials, and many other common function types.
Enter your function and integration variable to find the antiderivative. Results are displayed in clear mathematical notation with the constant of integration included.
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Integration is the reverse of differentiation. The indefinite integral (antiderivative) of a function f(x) is a function F(x) such that F'(x) = f(x). The result always includes an arbitrary constant C because the derivative of any constant is zero.
The Fundamental Theorem of Calculus connects differentiation and integration: if F is an antiderivative of f, then the definite integral from a to b of f(x)dx = F(b) - F(a).
Aufgabe: Find the integral of x^3
Loesung: Using the power rule: integral of x^n = x^(n+1)/(n+1) + C
Antwort: x^4/4 + C
Aufgabe: Find the integral of cos(x)
Loesung: The antiderivative of cos(x) is sin(x)
Antwort: sin(x) + C
Aufgabe: Find the integral of 3x^2 + 2x - 5
Loesung: Integrate term by term: 3*x^3/3 + 2*x^2/2 - 5x
Antwort: x^3 + x^2 - 5x + C
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