Potenzregel der Integralrechnung
The potenzregel integral beispiel shows that for a function f(x) = x², the corresponding stammfunktion berechnen is F(x) = (x³)/3. When we take the derivative of F(x) with respect to x, we get back to the original function f(x), as expected.
Summenregel der Integralrechnung
In the summenregel integral beweis, for a function f(x) = x¹ + x², the stammfunktion berechnen is F(x) = (x²)/2 + (x³)/3. The derivative of F(x) with respect to x yields back the original function f(x), proving the validity of the summenregel.
Faktorregel der Integralrechnung
The faktorregel integral beispiel demonstrates that for a function f(x) = 5x², the stammfunktion berechnen is F(x) = (5x³)/3. This follows the faktorregel integral, and the derivative of F(x) with respect to x returns the original function f(x).
Exponentialregel der Integralrechnung
In the exponentialregel integral beispiel, for a function f(x) = e^2x, the stammfunktion berechnen is F(x) = (1/2) e^2x. The derivative of F(x) with respect to x verifies the correctness of the exponentialregel.
Sinusregel und Kosinusregel der Integralrechnung
Applying the sinusregel and kosinusregel integral regeln to the function f(x) = 3 cos (3x²) results in the stammfunktion berechnen F(x) = (1/3) sin (3x³) + C, where C is the constant of integration. The derivative of F(x) confirms that the original function is recovered, thus validating the sinusregel and kosinusregel integralrechner.
By understanding and applying these integral regeln, mathematicians and scientists can efficiently solve complex mathematical problems involving integrals and stammfunktionen.
