$$$\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000}$$$의 적분
관련 계산기: 정적분 및 가적분 계산기
사용자 입력
$$$\int \frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000}\, dt$$$을(를) 구하시오.
풀이
상수배 법칙 $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$을 $$$c=\frac{1003605945944011425233769242881280649744658171441}{1000000000000000000000000000000000000000000000000}$$$와 $$$f{\left(t \right)} = t$$$에 적용하세요:
$${\color{red}{\int{\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000} d t}}} = {\color{red}{\left(\frac{1003605945944011425233769242881280649744658171441 \int{t d t}}{1000000000000000000000000000000000000000000000000}\right)}}$$
멱법칙($$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=1$$$에 적용합니다:
$$\frac{1003605945944011425233769242881280649744658171441 {\color{red}{\int{t d t}}}}{1000000000000000000000000000000000000000000000000}=\frac{1003605945944011425233769242881280649744658171441 {\color{red}{\frac{t^{1 + 1}}{1 + 1}}}}{1000000000000000000000000000000000000000000000000}=\frac{1003605945944011425233769242881280649744658171441 {\color{red}{\left(\frac{t^{2}}{2}\right)}}}{1000000000000000000000000000000000000000000000000}$$
따라서,
$$\int{\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000} d t} = \frac{1003605945944011425233769242881280649744658171441 t^{2}}{2000000000000000000000000000000000000000000000000}$$
적분 상수를 추가하세요:
$$\int{\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000} d t} = \frac{1003605945944011425233769242881280649744658171441 t^{2}}{2000000000000000000000000000000000000000000000000}+C$$
정답
$$$\int \frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000}\, dt = \frac{1003605945944011425233769242881280649744658171441 t^{2}}{2000000000000000000000000000000000000000000000000} + C$$$A