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