Integral of $$$b d m o x$$$ with respect to $$$x$$$

Find $$$\int b d m o x\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=b d m o$$$ and $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{b d m o x d x}}} = {\color{red}{b d m o \int{x d x}}}$$

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=1$$$:

$$b d m o {\color{red}{\int{x d x}}}=b d m o {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=b d m o {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

Therefore,

$$\int{b d m o x d x} = \frac{b d m o x^{2}}{2}$$

Add the constant of integration:

$$\int{b d m o x d x} = \frac{b d m o x^{2}}{2}+C$$

$$$\int b d m o x\, dx = \frac{b d m o x^{2}}{2} + C$$$A