Integral de $$$\frac{s^{2}}{d t}$$$ con respecto a $$$t$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{s^{2}}{d t}\, dt$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ con $$$c=\frac{s^{2}}{d}$$$ y $$$f{\left(t \right)} = \frac{1}{t}$$$:
$${\color{red}{\int{\frac{s^{2}}{d t} d t}}} = {\color{red}{\frac{s^{2} \int{\frac{1}{t} d t}}{d}}}$$
La integral de $$$\frac{1}{t}$$$ es $$$\int{\frac{1}{t} d t} = \ln{\left(\left|{t}\right| \right)}$$$:
$$\frac{s^{2} {\color{red}{\int{\frac{1}{t} d t}}}}{d} = \frac{s^{2} {\color{red}{\ln{\left(\left|{t}\right| \right)}}}}{d}$$
Por lo tanto,
$$\int{\frac{s^{2}}{d t} d t} = \frac{s^{2} \ln{\left(\left|{t}\right| \right)}}{d}$$
Añade la constante de integración:
$$\int{\frac{s^{2}}{d t} d t} = \frac{s^{2} \ln{\left(\left|{t}\right| \right)}}{d}+C$$
Respuesta
$$$\int \frac{s^{2}}{d t}\, dt = \frac{s^{2} \ln\left(\left|{t}\right|\right)}{d} + C$$$A