Integral of $$$i n t x^{2} の$$$ with respect to $$$x$$$

Find $$$\int i n t x^{2} の\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=i n t の$$$ and $$$f{\left(x \right)} = x^{2}$$$:

$${\color{red}{\int{i n t x^{2} の d x}}} = {\color{red}{i n t の \int{x^{2} d x}}}$$

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=2$$$:

$$i n t の {\color{red}{\int{x^{2} d x}}}=i n t の {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}=i n t の {\color{red}{\left(\frac{x^{3}}{3}\right)}}$$

Therefore,

$$\int{i n t x^{2} の d x} = \frac{i n t x^{3} の}{3}$$

Add the constant of integration:

$$\int{i n t x^{2} の d x} = \frac{i n t x^{3} の}{3}+C$$

$$$\int i n t x^{2} の\, dx = \frac{i n t x^{3} の}{3} + C$$$A