$$$62 x + \left(12 x - 12\right) e^{2} - 62$$$의 적분

$$$\int \left(62 x + \left(12 x - 12\right) e^{2} - 62\right)\, dx$$$을(를) 구하시오.

각 항별로 적분하십시오:

$${\color{red}{\int{\left(62 x + \left(12 x - 12\right) e^{2} - 62\right)d x}}} = {\color{red}{\left(- \int{62 d x} + \int{62 x d x} + \int{\left(12 x - 12\right) e^{2} d x}\right)}}$$

상수 법칙 $$$\int c\, dx = c x$$$을 $$$c=62$$$에 적용하십시오:

$$\int{62 x d x} + \int{\left(12 x - 12\right) e^{2} d x} - {\color{red}{\int{62 d x}}} = \int{62 x d x} + \int{\left(12 x - 12\right) e^{2} d x} - {\color{red}{\left(62 x\right)}}$$

상수배 법칙 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$을 $$$c=62$$$와 $$$f{\left(x \right)} = x$$$에 적용하세요:

$$- 62 x + \int{\left(12 x - 12\right) e^{2} d x} + {\color{red}{\int{62 x d x}}} = - 62 x + \int{\left(12 x - 12\right) e^{2} d x} + {\color{red}{\left(62 \int{x d x}\right)}}$$

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=1$$$에 적용합니다:

$$- 62 x + \int{\left(12 x - 12\right) e^{2} d x} + 62 {\color{red}{\int{x d x}}}=- 62 x + \int{\left(12 x - 12\right) e^{2} d x} + 62 {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=- 62 x + \int{\left(12 x - 12\right) e^{2} d x} + 62 {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

피적분함수를 단순화하세요.:

$$31 x^{2} - 62 x + {\color{red}{\int{\left(12 x - 12\right) e^{2} d x}}} = 31 x^{2} - 62 x + {\color{red}{\int{12 \left(x - 1\right) e^{2} d x}}}$$

상수배 법칙 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$을 $$$c=12 e^{2}$$$와 $$$f{\left(x \right)} = x - 1$$$에 적용하세요:

$$31 x^{2} - 62 x + {\color{red}{\int{12 \left(x - 1\right) e^{2} d x}}} = 31 x^{2} - 62 x + {\color{red}{\left(12 e^{2} \int{\left(x - 1\right)d x}\right)}}$$

각 항별로 적분하십시오:

$$31 x^{2} - 62 x + 12 e^{2} {\color{red}{\int{\left(x - 1\right)d x}}} = 31 x^{2} - 62 x + 12 e^{2} {\color{red}{\left(- \int{1 d x} + \int{x d x}\right)}}$$

상수 법칙 $$$\int c\, dx = c x$$$을 $$$c=1$$$에 적용하십시오:

$$31 x^{2} - 62 x + 12 e^{2} \left(\int{x d x} - {\color{red}{\int{1 d x}}}\right) = 31 x^{2} - 62 x + 12 e^{2} \left(\int{x d x} - {\color{red}{x}}\right)$$

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=1$$$에 적용합니다:

$$31 x^{2} - 62 x + 12 e^{2} \left(- x + {\color{red}{\int{x d x}}}\right)=31 x^{2} - 62 x + 12 e^{2} \left(- x + {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}\right)=31 x^{2} - 62 x + 12 e^{2} \left(- x + {\color{red}{\left(\frac{x^{2}}{2}\right)}}\right)$$

따라서,

$$\int{\left(62 x + \left(12 x - 12\right) e^{2} - 62\right)d x} = 31 x^{2} - 62 x + 12 \left(\frac{x^{2}}{2} - x\right) e^{2}$$

간단히 하시오:

$$\int{\left(62 x + \left(12 x - 12\right) e^{2} - 62\right)d x} = x \left(31 + 6 e^{2}\right) \left(x - 2\right)$$

적분 상수를 추가하세요:

$$\int{\left(62 x + \left(12 x - 12\right) e^{2} - 62\right)d x} = x \left(31 + 6 e^{2}\right) \left(x - 2\right)+C$$

$$$\int \left(62 x + \left(12 x - 12\right) e^{2} - 62\right)\, dx = x \left(31 + 6 e^{2}\right) \left(x - 2\right) + C$$$A