Integral dari $$$1 - 112 x^{3}$$$

Temukan $$$\int \left(1 - 112 x^{3}\right)\, dx$$$.

Integralkan suku demi suku:

$${\color{red}{\int{\left(1 - 112 x^{3}\right)d x}}} = {\color{red}{\left(\int{1 d x} - \int{112 x^{3} d x}\right)}}$$

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

$$- \int{112 x^{3} d x} + {\color{red}{\int{1 d x}}} = - \int{112 x^{3} d x} + {\color{red}{x}}$$

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=112$$$ dan $$$f{\left(x \right)} = x^{3}$$$:

$$x - {\color{red}{\int{112 x^{3} d x}}} = x - {\color{red}{\left(112 \int{x^{3} d x}\right)}}$$

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

$$x - 112 {\color{red}{\int{x^{3} d x}}}=x - 112 {\color{red}{\frac{x^{1 + 3}}{1 + 3}}}=x - 112 {\color{red}{\left(\frac{x^{4}}{4}\right)}}$$

Oleh karena itu,

$$\int{\left(1 - 112 x^{3}\right)d x} = - 28 x^{4} + x$$

Tambahkan konstanta integrasi:

$$\int{\left(1 - 112 x^{3}\right)d x} = - 28 x^{4} + x+C$$

$$$\int \left(1 - 112 x^{3}\right)\, dx = \left(- 28 x^{4} + x\right) + C$$$A