Integral de $$$\frac{\sqrt{15}}{15 \sqrt{x}}$$$

Halla $$$\int \frac{\sqrt{15}}{15 \sqrt{x}}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=\frac{\sqrt{15}}{15}$$$ y $$$f{\left(x \right)} = \frac{1}{\sqrt{x}}$$$:

$${\color{red}{\int{\frac{\sqrt{15}}{15 \sqrt{x}} d x}}} = {\color{red}{\left(\frac{\sqrt{15} \int{\frac{1}{\sqrt{x}} d x}}{15}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=- \frac{1}{2}$$$:

$$\frac{\sqrt{15} {\color{red}{\int{\frac{1}{\sqrt{x}} d x}}}}{15}=\frac{\sqrt{15} {\color{red}{\int{x^{- \frac{1}{2}} d x}}}}{15}=\frac{\sqrt{15} {\color{red}{\frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1}}}}{15}=\frac{\sqrt{15} {\color{red}{\left(2 x^{\frac{1}{2}}\right)}}}{15}=\frac{\sqrt{15} {\color{red}{\left(2 \sqrt{x}\right)}}}{15}$$

Por lo tanto,

$$\int{\frac{\sqrt{15}}{15 \sqrt{x}} d x} = \frac{2 \sqrt{15} \sqrt{x}}{15}$$

Añade la constante de integración:

$$\int{\frac{\sqrt{15}}{15 \sqrt{x}} d x} = \frac{2 \sqrt{15} \sqrt{x}}{15}+C$$

$$$\int \frac{\sqrt{15}}{15 \sqrt{x}}\, dx = \frac{2 \sqrt{15} \sqrt{x}}{15} + C$$$A