$$$\frac{4}{\sqrt{1 - x^{2}}}$$$의 적분

$$$\int \frac{4}{\sqrt{1 - x^{2}}}\, dx$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$을 $$$c=4$$$와 $$$f{\left(x \right)} = \frac{1}{\sqrt{1 - x^{2}}}$$$에 적용하세요:

$${\color{red}{\int{\frac{4}{\sqrt{1 - x^{2}}} d x}}} = {\color{red}{\left(4 \int{\frac{1}{\sqrt{1 - x^{2}}} d x}\right)}}$$

$$$\frac{1}{\sqrt{1 - x^{2}}}$$$의 적분은 $$$\int{\frac{1}{\sqrt{1 - x^{2}}} d x} = \operatorname{asin}{\left(x \right)}$$$:

$$4 {\color{red}{\int{\frac{1}{\sqrt{1 - x^{2}}} d x}}} = 4 {\color{red}{\operatorname{asin}{\left(x \right)}}}$$

따라서,

$$\int{\frac{4}{\sqrt{1 - x^{2}}} d x} = 4 \operatorname{asin}{\left(x \right)}$$

적분 상수를 추가하세요:

$$\int{\frac{4}{\sqrt{1 - x^{2}}} d x} = 4 \operatorname{asin}{\left(x \right)}+C$$

$$$\int \frac{4}{\sqrt{1 - x^{2}}}\, dx = 4 \operatorname{asin}{\left(x \right)} + C$$$A