Integral of $$$2 x^{213}$$$

Find $$$\int 2 x^{213}\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=2$$$ and $$$f{\left(x \right)} = x^{213}$$$:

$${\color{red}{\int{2 x^{213} d x}}} = {\color{red}{\left(2 \int{x^{213} d x}\right)}}$$

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=213$$$:

$$2 {\color{red}{\int{x^{213} d x}}}=2 {\color{red}{\frac{x^{1 + 213}}{1 + 213}}}=2 {\color{red}{\left(\frac{x^{214}}{214}\right)}}$$

Therefore,

$$\int{2 x^{213} d x} = \frac{x^{214}}{107}$$

Add the constant of integration:

$$\int{2 x^{213} d x} = \frac{x^{214}}{107}+C$$

$$$\int 2 x^{213}\, dx = \frac{x^{214}}{107} + C$$$A