Integral dari $$$\frac{x}{2 k + 1}$$$ terhadap $$$x$$$

Temukan $$$\int \frac{x}{2 k + 1}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=\frac{1}{2 k + 1}$$$ dan $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{\frac{x}{2 k + 1} d x}}} = {\color{red}{\frac{\int{x d x}}{2 k + 1}}}$$

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

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

Oleh karena itu,

$$\int{\frac{x}{2 k + 1} d x} = \frac{x^{2}}{2 \left(2 k + 1\right)}$$

Tambahkan konstanta integrasi:

$$\int{\frac{x}{2 k + 1} d x} = \frac{x^{2}}{2 \left(2 k + 1\right)}+C$$

$$$\int \frac{x}{2 k + 1}\, dx = \frac{x^{2}}{2 \left(2 k + 1\right)} + C$$$A