Integral dari $$$x^{2} - 1$$$

Temukan $$$\int \left(x^{2} - 1\right)\, dx$$$.

Integralkan suku demi suku:

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

Terapkan aturan konstanta $$$\int c\, dx = c x$$$ dengan $$$c=1$$$:

$$\int{x^{2} d x} - {\color{red}{\int{1 d x}}} = \int{x^{2} d x} - {\color{red}{x}}$$

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

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

Oleh karena itu,

$$\int{\left(x^{2} - 1\right)d x} = \frac{x^{3}}{3} - x$$

Tambahkan konstanta integrasi:

$$\int{\left(x^{2} - 1\right)d x} = \frac{x^{3}}{3} - x+C$$

$$$\int \left(x^{2} - 1\right)\, dx = \left(\frac{x^{3}}{3} - x\right) + C$$$A