Integral de $$$- \sqrt{x} \tan{\left(1 \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \left(- \sqrt{x} \tan{\left(1 \right)}\right)\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=- \tan{\left(1 \right)}$$$ y $$$f{\left(x \right)} = \sqrt{x}$$$:
$${\color{red}{\int{\left(- \sqrt{x} \tan{\left(1 \right)}\right)d x}}} = {\color{red}{\left(- \tan{\left(1 \right)} \int{\sqrt{x} d x}\right)}}$$
Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=\frac{1}{2}$$$:
$$- \tan{\left(1 \right)} {\color{red}{\int{\sqrt{x} d x}}}=- \tan{\left(1 \right)} {\color{red}{\int{x^{\frac{1}{2}} d x}}}=- \tan{\left(1 \right)} {\color{red}{\frac{x^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}}}=- \tan{\left(1 \right)} {\color{red}{\left(\frac{2 x^{\frac{3}{2}}}{3}\right)}}$$
Por lo tanto,
$$\int{\left(- \sqrt{x} \tan{\left(1 \right)}\right)d x} = - \frac{2 x^{\frac{3}{2}} \tan{\left(1 \right)}}{3}$$
Añade la constante de integración:
$$\int{\left(- \sqrt{x} \tan{\left(1 \right)}\right)d x} = - \frac{2 x^{\frac{3}{2}} \tan{\left(1 \right)}}{3}+C$$
Respuesta
$$$\int \left(- \sqrt{x} \tan{\left(1 \right)}\right)\, dx = - \frac{2 x^{\frac{3}{2}} \tan{\left(1 \right)}}{3} + C$$$A