Integral de $$$\frac{3 a l m}{16 \pi^{2}}$$$ con respecto a $$$a$$$

Halla $$$\int \frac{3 a l m}{16 \pi^{2}}\, da$$$.

Aplica la regla del factor constante $$$\int c f{\left(a \right)}\, da = c \int f{\left(a \right)}\, da$$$ con $$$c=\frac{3 l m}{16 \pi^{2}}$$$ y $$$f{\left(a \right)} = a$$$:

$${\color{red}{\int{\frac{3 a l m}{16 \pi^{2}} d a}}} = {\color{red}{\left(\frac{3 l m \int{a d a}}{16 \pi^{2}}\right)}}$$

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

$$\frac{3 l m {\color{red}{\int{a d a}}}}{16 \pi^{2}}=\frac{3 l m {\color{red}{\frac{a^{1 + 1}}{1 + 1}}}}{16 \pi^{2}}=\frac{3 l m {\color{red}{\left(\frac{a^{2}}{2}\right)}}}{16 \pi^{2}}$$

Por lo tanto,

$$\int{\frac{3 a l m}{16 \pi^{2}} d a} = \frac{3 a^{2} l m}{32 \pi^{2}}$$

Añade la constante de integración:

$$\int{\frac{3 a l m}{16 \pi^{2}} d a} = \frac{3 a^{2} l m}{32 \pi^{2}}+C$$

$$$\int \frac{3 a l m}{16 \pi^{2}}\, da = \frac{3 a^{2} l m}{32 \pi^{2}} + C$$$A