Integral dari $$$412 x^{\frac{3}{2}}$$$

Temukan $$$\int 412 x^{\frac{3}{2}}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=412$$$ dan $$$f{\left(x \right)} = x^{\frac{3}{2}}$$$:

$${\color{red}{\int{412 x^{\frac{3}{2}} d x}}} = {\color{red}{\left(412 \int{x^{\frac{3}{2}} d x}\right)}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=\frac{3}{2}$$$:

$$412 {\color{red}{\int{x^{\frac{3}{2}} d x}}}=412 {\color{red}{\frac{x^{1 + \frac{3}{2}}}{1 + \frac{3}{2}}}}=412 {\color{red}{\left(\frac{2 x^{\frac{5}{2}}}{5}\right)}}$$

Oleh karena itu,

$$\int{412 x^{\frac{3}{2}} d x} = \frac{824 x^{\frac{5}{2}}}{5}$$

Tambahkan konstanta integrasi:

$$\int{412 x^{\frac{3}{2}} d x} = \frac{824 x^{\frac{5}{2}}}{5}+C$$

$$$\int 412 x^{\frac{3}{2}}\, dx = \frac{824 x^{\frac{5}{2}}}{5} + C$$$A