Integral of $$$\frac{a^{3} \ln\left(x\right)}{x}$$$ with respect to $$$e$$$

Find $$$\int \frac{a^{3} \ln\left(x\right)}{x}\, de$$$.

Apply the constant rule $$$\int c\, de = c e$$$ with $$$c=\frac{a^{3} \ln{\left(x \right)}}{x}$$$:

$${\color{red}{\int{\frac{a^{3} \ln{\left(x \right)}}{x} d e}}} = {\color{red}{\frac{a^{3} e \ln{\left(x \right)}}{x}}}$$

Therefore,

$$\int{\frac{a^{3} \ln{\left(x \right)}}{x} d e} = \frac{a^{3} e \ln{\left(x \right)}}{x}$$

Add the constant of integration:

$$\int{\frac{a^{3} \ln{\left(x \right)}}{x} d e} = \frac{a^{3} e \ln{\left(x \right)}}{x}+C$$

$$$\int \frac{a^{3} \ln\left(x\right)}{x}\, de = \frac{a^{3} e \ln\left(x\right)}{x} + C$$$A