Integral dari $$$i a n t x^{3} - 7$$$ terhadap $$$x$$$

Temukan $$$\int \left(i a n t x^{3} - 7\right)\, dx$$$.

Integralkan suku demi suku:

$${\color{red}{\int{\left(i a n t x^{3} - 7\right)d x}}} = {\color{red}{\left(- \int{7 d x} + \int{i a n t x^{3} d x}\right)}}$$

Terapkan aturan konstanta $$$\int c\, dx = c x$$$ dengan $$$c=7$$$:

$$\int{i a n t x^{3} d x} - {\color{red}{\int{7 d x}}} = \int{i a n t x^{3} d x} - {\color{red}{\left(7 x\right)}}$$

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

$$- 7 x + {\color{red}{\int{i a n t x^{3} d x}}} = - 7 x + {\color{red}{i a n t \int{x^{3} d x}}}$$

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

$$i a n t {\color{red}{\int{x^{3} d x}}} - 7 x=i a n t {\color{red}{\frac{x^{1 + 3}}{1 + 3}}} - 7 x=i a n t {\color{red}{\left(\frac{x^{4}}{4}\right)}} - 7 x$$

Oleh karena itu,

$$\int{\left(i a n t x^{3} - 7\right)d x} = \frac{i a n t x^{4}}{4} - 7 x$$

Sederhanakan:

$$\int{\left(i a n t x^{3} - 7\right)d x} = \frac{x \left(i a n t x^{3} - 28\right)}{4}$$

Tambahkan konstanta integrasi:

$$\int{\left(i a n t x^{3} - 7\right)d x} = \frac{x \left(i a n t x^{3} - 28\right)}{4}+C$$

$$$\int \left(i a n t x^{3} - 7\right)\, dx = \frac{x \left(i a n t x^{3} - 28\right)}{4} + C$$$A