Integral dari $$$x^{\theta - 1}$$$ terhadap $$$x$$$

Temukan $$$\int x^{\theta - 1}\, dx$$$.

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

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

Oleh karena itu,

$$\int{x^{\theta - 1} d x} = \frac{x^{\theta}}{\theta}$$

Tambahkan konstanta integrasi:

$$\int{x^{\theta - 1} d x} = \frac{x^{\theta}}{\theta}+C$$

$$$\int x^{\theta - 1}\, dx = \frac{x^{\theta}}{\theta} + C$$$A